Why some people still don't want to wear mask?

[jobo]

That's the problem that exists in society. Someone states a fact, then you ask them to check it out. Instead of doing that, they dance around it.

Then they try to turn it back around on you. An example of that is. his statement to you. "well it doesnt always, im suprised you dont know that,? perhaps youd like to pick up the mantal and prove it does?" None of that involves him solving 2+2=

but its not a fact that 2 plus two equals 4.

ive told you that several times, but your that dim its not sinking in, if your counting in binary the answer is 0100, if your counting in base three, the answer is 11

 

[Steve]

but its not a fact that 2 plus two equals 4.

ive told you that several times, but your that dim its not sinking in, if your counting in binary the answer is 0100, if your counting in base three, the answer is 11

Hey man. Keep those personal attacks up and you're going to get this interesting thread locked.

 

[EdwardA]

Sometimes it's 8/4 + 8/4 =4, but what I see a lot of, one guy will see 5 facts that agree with his position and say here are the facts, I'm right. The other guy on the opposite side sees 5 facts that supports his side and says, no I'm right. Trouble is, neither dug deep enough to find the 20 facts that make up the issue. It takes more effort and honest neutrality than either applied.

Only those willing to set aside their own opinions can find the truth. ...and a lot of work.

 

[jobo]

Hey man. Keep those personal attacks up and you're going to get this interesting thread locked.

yea but he is thick as pig****, sometimes you have to bite the bullet

 

[drop bear]

they are a cross section of the public, that they are so suspicous of the govenment is a failure by the govenment, who have to goven by consent and they have very little as things stand

it doesnt matter if you are morally and factually correct, if no one belives you

Not really. Again you are suggesting that there is an onus on experts is to convince idiots.

Unfortunately the idiots don't make that possible.

Sorry can you please explain a concept that took you 4 years of specialized training to understand in about ten seconds?

I just have a really short attention span.



So for example.

"To come up with a proof of such a seemingly simple fact as 2+2=4" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">2+2=42+2=4, we need a set of axioms to start with, and we need precise definitions of all the terms we are using. Depending on what set of axioms you start with, proving that 2+2=4" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">2+2=42+2=4, and that no other natural number can equal 2+2" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">2+22+2 may be either very simple or surprisingly difficult. For example in Russell and Whitehead's Principia, it famously took over 300 pages of work before they could prove that 1+1=2" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">1+1=21+1=2. They started with a very sparse set of axioms though.

The most common set of axioms for the natural numbers are the Peano Axioms.

They are

1. 0" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">00 is a natural number.
2. For every natural number x" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">xx, x=x" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">x=xx=x.
3. For all natural numbers x" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">xx and y" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">yy, if x=y" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">x=yx=y, then y=x" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">y=xy=x.
4. For all natural numbers x" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">xx, y" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">yy, and z" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">zz, if x=y" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">x=yx=y and y=z" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">y=zy=z, then x=z" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">x=zx=z.
5. For all a" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">aa and b" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">bb, if a" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">aa is a natural number, and a=b" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">a=ba=b, then b" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">bb is a natural number.
6. For every natural number n" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">nn, S(n)" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">S(n)S(n) is a natural number.
7. For every natural number n" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">nn, S(n)=0" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">S(n)=0S(n)=0 is false.
8. For all natural numbers m" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">mm and n" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">nn, if S(m)=S(n)" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">S(m)=S(n)S(m)=S(n) then m=n" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">m=nm=n.
9. If K" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">KK is a set such that 0∈K" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">0∈K0∈K, and for every natural number n" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">nn, n∈K" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">n∈Kn∈K implies that S(n)∈K" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">S(n)∈KS(n)∈K, then K" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">KK contains all natural numbers.

Here S" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">SS is the successor function, it takes each natural number to its successor. This might seem like a complicated mess compared to the simplicity of natural numbers, but we need to be precise. We need to carefully construct the axioms so that no contradiction can be derived from them, and so they encapsulate what we understand to be the natural numbers. We want to be able to prove interesting statements about the natural numbers from them. Note that the axioms contain undefined terms. The axioms don't need to state what the terms mean, only what they do.

The following definitions are commonly used within this axiomatization. They are the definitions from Peano's original paper (An English translation is available in the book From Frege to Gödel), modified to start at 0" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">00 instead of 1" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">11.

1" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">11 is defined as S(0)" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">S(0)S(0), 2" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">22 is defined as S(1)" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">S(1)S(1), 3" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">33 is defined as S(2)" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">S(2)S(2), and 4" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">44 is defined as S(3)" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">S(3)S(3). Addition is defined recursively as follows.


a+0=a" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">a+0=aa+0=a
a+S(b)=S(a+b)" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">a+S(b)=S(a+b)a+S(b)=S(a+b)
.


Thus


2+2=2+S(1)=S(2+1)=S(2+S(0))=S(S(2+0))=S(S(2))=S(3)=4" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative; display: table-cell !important; width: 10000em !important;">2+2=2+S(1)=S(2+1)=S(2+S(0))=S(S(2+0))=S(S(2))=S(3)=42+2=2+S(1)=S(2+1)=S(2+S(0))=S(S(2+0))=S(S(2))=S(3)=4


proving that 2+2=4" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">2+2=42+2=4.

This is the unique value of 2+2" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">2+22+2 by axiom 4.

If x=2+2" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">x=2+2x=2+2 and 2+2=4" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">2+2=42+2=4, then x=4" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">x=4x=4."

 

[jobo]

Not really. Again you are suggesting that there is an onus on experts is to convince idiots.

Unfortunately the idiots don't make that possible.

Sorry can you please explain a concept that took you 4 years of specialized training to understand in about ten seconds?

I just have a really short attention span.



So for example.

"To come up with a proof of such a seemingly simple fact as 2+2=4" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">2+2=42+2=4, we need a set of axioms to start with, and we need precise definitions of all the terms we are using. Depending on what set of axioms you start with, proving that 2+2=4" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">2+2=42+2=4, and that no other natural number can equal 2+2" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">2+22+2 may be either very simple or surprisingly difficult. For example in Russell and Whitehead's Principia, it famously took over 300 pages of work before they could prove that 1+1=2" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">1+1=21+1=2. They started with a very sparse set of axioms though.

The most common set of axioms for the natural numbers are the Peano Axioms.

They are

1. 0" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">00 is a natural number.
2. For every natural number x" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">xx, x=x" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">x=xx=x.
3. For all natural numbers x" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">xx and y" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">yy, if x=y" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">x=yx=y, then y=x" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">y=xy=x.
4. For all natural numbers x" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">xx, y" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">yy, and z" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">zz, if x=y" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">x=yx=y and y=z" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">y=zy=z, then x=z" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">x=zx=z.
5. For all a" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">aa and b" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">bb, if a" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">aa is a natural number, and a=b" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">a=ba=b, then b" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">bb is a natural number.
6. For every natural number n" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">nn, S(n)" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">S(n)S(n) is a natural number.
7. For every natural number n" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">nn, S(n)=0" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">S(n)=0S(n)=0 is false.
8. For all natural numbers m" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">mm and n" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">nn, if S(m)=S(n)" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">S(m)=S(n)S(m)=S(n) then m=n" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">m=nm=n.
9. If K" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">KK is a set such that 0∈K" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">0∈K0∈K, and for every natural number n" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">nn, n∈K" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">n∈Kn∈K implies that S(n)∈K" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">S(n)∈KS(n)∈K, then K" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">KK contains all natural numbers.

Here S" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">SS is the successor function, it takes each natural number to its successor. This might seem like a complicated mess compared to the simplicity of natural numbers, but we need to be precise. We need to carefully construct the axioms so that no contradiction can be derived from them, and so they encapsulate what we understand to be the natural numbers. We want to be able to prove interesting statements about the natural numbers from them. Note that the axioms contain undefined terms. The axioms don't need to state what the terms mean, only what they do.

The following definitions are commonly used within this axiomatization. They are the definitions from Peano's original paper (An English translation is available in the book From Frege to Gödel), modified to start at 0" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">00 instead of 1" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">11.

1" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">11 is defined as S(0)" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">S(0)S(0), 2" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">22 is defined as S(1)" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">S(1)S(1), 3" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">33 is defined as S(2)" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">S(2)S(2), and 4" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">44 is defined as S(3)" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">S(3)S(3). Addition is defined recursively as follows.


a+0=a" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">a+0=aa+0=a
a+S(b)=S(a+b)" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">a+S(b)=S(a+b)a+S(b)=S(a+b)
.


Thus


2+2=2+S(1)=S(2+1)=S(2+S(0))=S(S(2+0))=S(S(2))=S(3)=4" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative; display: table-cell !important; width: 10000em !important;">2+2=2+S(1)=S(2+1)=S(2+S(0))=S(S(2+0))=S(S(2))=S(3)=42+2=2+S(1)=S(2+1)=S(2+S(0))=S(S(2+0))=S(S(2))=S(3)=4


proving that 2+2=4" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">2+2=42+2=4.

This is the unique value of 2+2" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">2+22+2 by axiom 4.

If x=2+2" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">x=2+2x=2+2 and 2+2=4" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">2+2=42+2=4, then x=4" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">x=4x=4."

no its the job of govenments to carry the bulk of the population with them.

if people idiots or otherwise dont belive what a govenment tells them, then at best they dont get relected at worsr you get a compkete breakdown in civil order, or anywhere in between, thats the nature of democracy, you dont need to believe what the govenment tells you

the govenment need to lead, if no one follows it tends to end badly

 

[dvcochran]

There are a lot of facts that are not subject to interpretation. It's a fact that in general if you break the law you will have a legal penalty for doing so. It's a fact that you woke up today unless you haven't been to sleep since yesterday. It's a fact that driving while drunk increases your risk of having an accident. It's a fact that 2+2=4.

It's not difficult to know which facts are actual factual as we speak. That is controlled by the level of knowledge and ignorance you have on a subject. There are people who dismiss fact out of ignorance, and there are who would rather that you don't know the truth. But none of that changes what really happened. 2+2=4 even if a person chooses not to believe that.

if you break the law you will have a legal penalty for doing so.

My wife is an attorney. She busted a gut when I showed that one. It would be nice if the world was that concrete. Boring but much better.

 

[jobo]

My wife is an attorney. She busted a gut when I showed that one. It would be nice if the world was that concrete. Boring but much better.

can you get her to tell him you need to be convicted before you get fined, if indeed you get caught at all

 

[JowGaWolf]

My wife is an attorney. She busted a gut when I showed that one. It would be nice if the world was that concrete. Boring but much better.

Yeah. What can I say. I could have gone into more specifics and exceptions. That just seemed too complicated. Law is already complex enough as it is. I try to keep it as simple as possible. There's a disagreement on 2+2=4, so I fear being more accurate about a discussion on law would be too much lol.

Tell your wife that I suffered 2 years of law classes with an attorney and I hated every minute of it. Every answer my professor had was a legal one and it was like she didn't have feelings. She was just straight to the point and very detailed. If the students had to give a definition or explain a case and the ruling (hated that too) then nothing less than detailed answer was accepted. It was like 2 years of being wrong, assumptions weren't allowed, emotions weren't allowed. So I'm happy that she could have to good chuckle.

 

[JowGaWolf]

My wife is an attorney. She busted a gut when I showed that one. It would be nice if the world was that concrete. Boring but much better.

"can you get her to tell him you need to be convicted before you get fined, if indeed you get caught at al" So Jobo just posted this, and I can already here my law professor lol.

• what are the laws of the where it occurred? Sate? City? Country? What was the offense? How does the jurisdiction view the offense? what is the classification of it?. Is it criminal or civil?

Then everything after that would be. - nope you got that wrong or not always, or according to legal statues, rulings, and a lot of other stuff that would just make me say. Yeah. you hand that stuff. Only if you want, because I can't pay you lol.

The first lesson of my legal education was to never start an argument with " Can you (the legal expert) tell (some other person) that A has to happen before B happens" that an never get into and argument with a lawyer about law. lol.

 

[JowGaWolf]

It would be nice if the world was that concrete. Boring but much better.

It would be nice then I could argue with a lawyer lol. But unfortunately simple doesn't cover all necessary aspect of a law. Make a simple law and the next thing that happens are "What abouts?" and "What ifs" It's like a building a car with a person with never ending ideas of "wouldn't it be cool if we added..."

 

[JowGaWolf]

can you get her to tell him you need to be convicted before you get fined, if indeed you get caught at all

 

[jks9199]

Ladies & Gentlemen,
We have several open tickets on this thread. I've locked it so that I can go through it with a fine tooth comb. As a reminder, before I've had a chance to do more than glance over things... Political posting should go to US Message Board - Political Discussion Forum. And let's remember a few old rules for life:

• If you can't say something nice, don't say anything.
• If people are thinking you're foolish, why open your mouth and prove it?

The bottom line is that the current pandemic, and responses to it, are huge topics, with tons of opinions and even more emotional energy invested. Solid data is hard to find, and it's even harder to get people to think rationally, whichever side of the debate they are on, or whatever their opinion may be. Let's try to keep the discussions here civil and polite. While many might feel differently, it is possible to disagree with a person, and still treat them with respect and courtesy.

jks9199
MT Administrator

 

[jks9199]

All right, folks...

After a review, consider this a final warning. No more personal attacks. Keep the discussion courteous and polite. Much to my pleased amazement, y'all have done a decent job ducking politics. Keep that up.

NO MORE PERSONAL ATTACKS. Anyone making what the Moderation Team identifies as a personal attack will get points from this post on.

jks9199
MT Administrator

And -- just in case I'm unclear:
NO MORE PERSONAL ATTACKS!!

 

[EdwardA]

They unlocked this?

You can argue a point without pinning your disagreement on any one person. That's what I try...

At least most of us enjoyed ping pong. I'm pobably not any good at it any more. I was really good at pool once too. Then after a while, I lost the touch. Maybe I just got bored with both.

That's one thing I like about MA, there's many many things to train at.

 

[_Simon_]

MT... yeah....


You are my fire
The one desire
Believe when I say
I want it that way

But we are two worlds apart
Can't reach to your heart
When you say
That I want it that way

Tell me why
Ain't nothin' but a heartache
Tell me why
Ain't nothin' but a mistake
Tell me why
I never want to hear you say
I want it that way

Am I, your fire?
Your one, desire
Yes I know, it's too late
But I want it that way

Tell me why
Ain't nothin' but a heartache
Tell me why
Ain't nothin' but a mistake
Tell me why,
I never want to hear you say
I want it that way

Now I can see that we've fallen apart
From the way that it used to be, yeah
No matter the distance
I want you to know
That deep down inside of me

You are my fire
The one desire
You are (you are, you are, you are)

Don't want to hear you say
Ain't nothin' but a heartache
Ain't nothin' but a mistake
(Don't want to hear you say)
I never want to hear you say
I want it that way

Tell me why
Ain't nothin' but a heartache
Tell me why
Ain't nothin' but a mistake
Tell me why
I never want to hear you say
I want it that way

Tell me why
Ain't nothin' but a heartache
Ain't nothin' but a mistake
Tell me why
I never want to hear you say
(Never want to hear you say it)
I want it that way

'Cause I want it that way

 

[drop bear]

But the way the other way of looking at the 2+2=4 buisness is to use scientific method. Sort of. So you would conduct a series of experiments and if they corroborate each other then we can be fairly confident with an answer.

So we could look at
1+1+1+1=4
1+1=2
2+1+1=4
1+1+1+1=1+1+1+1.

And so on. And finding all this consistency we can conclude 2+2=4.

This is also the MMA for self defense argument.

Now go wear a mask. Or do MMA.

 

[EdwardA]

But the way the other way of looking at the 2+2=4 buisness is to use scientific method. Sort of. So you would conduct a series of experiments and if they corroborate each other then we can be fairly confident with an answer.

So we could look at
1+1+1+1=4
1+1=2
2+1+1=4
1+1+1+1=1+1+1+1.

And so on. And finding all this consistency we can conclude 2+2=4.

This is also the MMA for self defense argument.

Now go wear a mask. Or do MMA.

If it's law or required by the business where you are, wear one, if it's not, it's your choice no matter what anybody says.

√16 does too or (16/4 + 16/4)/2. Unlimited combos.

Just the other day, Fauci changed his mind again and said masks weren't very effective and that we should all be wearing full face shields. Who here is going to get one?

 

[_Simon_]

If it's law or required by the business where you are, wear one, if it's not, it's your choice no matter what anybody says.

√16 does too or (16/4 + 16/4)/2. Unlimited combos.

Just the other day, Fauci changed his mind again and said masks weren't very effective and that we should all be wearing full face shields. Who here is going to get one?

Ah what.. flip floppin, I actually like the idea of face shields, can actually see people's face and their expression, AND much easier to clean!

 

[jobo]

But the way the other way of looking at the 2+2=4 buisness is to use scientific method. Sort of. So you would conduct a series of experiments and if they corroborate each other then we can be fairly confident with an answer.

So we could look at
1+1+1+1=4
1+1=2
2+1+1=4
1+1+1+1=1+1+1+1.

And so on. And finding all this consistency we can conclude 2+2=4.

This is also the MMA for self defense argument.

Now go wear a mask. Or do MMA.

well that doesnt prove anything, it totally dependent on the coubrobg system you use

growing up we use based 12 for money and distance and base 16 for weight,

the americand still do for weight and distance

in base two its 0100, in base 3 its 11, in base 4 its 10. in base 16 its one quarter or .25 as well as 4, but all answers are correct unless the question specifies which units should be used for the answer

it only becomes a fact if you prefix it with "" in the base 10 system"

so as i said that fact is total dependent on interpretation