Last Poster #6

[Buka]

About a year ago, a young man who I knew causally at work, came up to me and said "I hear you're a guy who can get someone in shape". I said I was asked him what he needed.

He had just failed a fitness test for the FBI Academy- by one point. I said, "okay, we can do that, but we won't be going for one point, we'll be going to crush the fricken' thing. You game?" He was. We had three months. He wanted to know when we could start. I told him "Right now. And we don't do it the Law Enforcement way, we do it the Martial Arts way." I called his supervisor and said I needed him for twenty minutes, then called mine for a twenty minute relief.

Off we went to a storage area and started doing push ups, sit ups and pull ups. We did them every day at work, every day after work, every day when we were off. I did everything with him except the running - I don't run any more unless I'm chasing someone. I made him run while I yelled at him with a stopwatch in my hand.

God bless him, he showed up every day and worked his tail off. And he absolutely crushed that test, top of his class.

He graduated from the FBI Academy today. That's him on the left. Got me all teary eyed this morning.

 

[Steve]

About a year ago, a young man who I knew causally at work, came up to me and said "I hear you're a guy who can get someone in shape". I said I was asked him what he needed.

He had just failed a fitness test for the FBI Academy- by one point. I said, "okay, we can do that, but we won't be going for one point, we'll be going to crush the fricken' thing. You game?" He was. We had three months. He wanted to know when we could start. I told him "Right now. And we don't do it the Law Enforcement way, we do it the Martial Arts way." I called his supervisor and said I needed him for twenty minutes, then called mine for a twenty minute relief.

Off we went to a storage area and started doing push ups, sit ups and pull ups. We did them every day at work, every day after work, every day when we were off. I did everything with him except the running - I don't run any more unless I'm chasing someone. I made him run while I yelled at him with a stopwatch in my hand.

God bless him, he showed up every day and worked his tail off. And he absolutely crushed that test, top of his class.

He graduated from the FBI Academy today. That's him on the left. Got me all teary eyed this morning.

View attachment 23118

That's awesome.

 

[dvcochran]

About a year ago, a young man who I knew causally at work, came up to me and said "I hear you're a guy who can get someone in shape". I said I was asked him what he needed.

He had just failed a fitness test for the FBI Academy- by one point. I said, "okay, we can do that, but we won't be going for one point, we'll be going to crush the fricken' thing. You game?" He was. We had three months. He wanted to know when we could start. I told him "Right now. And we don't do it the Law Enforcement way, we do it the Martial Arts way." I called his supervisor and said I needed him for twenty minutes, then called mine for a twenty minute relief.

Off we went to a storage area and started doing push ups, sit ups and pull ups. We did them every day at work, every day after work, every day when we were off. I did everything with him except the running - I don't run any more unless I'm chasing someone. I made him run while I yelled at him with a stopwatch in my hand.

God bless him, he showed up every day and worked his tail off. And he absolutely crushed that test, top of his class.

He graduated from the FBI Academy today. That's him on the left. Got me all teary eyed this morning.

View attachment 23118

That is fantastic Buka Hell of a job to both of you.

 

[Buka]

That is fantastic Buka Hell of a job to both of you.

It's easy when the other guy has to do the work, but thanks.
I also told him that if the FBI ever wants to take me in, have them send that gal agent. I'd follow her anywhere.

 

[_Simon_]

About a year ago, a young man who I knew causally at work, came up to me and said "I hear you're a guy who can get someone in shape". I said I was asked him what he needed.

He had just failed a fitness test for the FBI Academy- by one point. I said, "okay, we can do that, but we won't be going for one point, we'll be going to crush the fricken' thing. You game?" He was. We had three months. He wanted to know when we could start. I told him "Right now. And we don't do it the Law Enforcement way, we do it the Martial Arts way." I called his supervisor and said I needed him for twenty minutes, then called mine for a twenty minute relief.

Off we went to a storage area and started doing push ups, sit ups and pull ups. We did them every day at work, every day after work, every day when we were off. I did everything with him except the running - I don't run any more unless I'm chasing someone. I made him run while I yelled at him with a stopwatch in my hand.

God bless him, he showed up every day and worked his tail off. And he absolutely crushed that test, top of his class.

He graduated from the FBI Academy today. That's him on the left. Got me all teary eyed this morning.

View attachment 23118

Oh man that is so darn cool.... such a nice thing to hear

 

[_Simon_]

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."

The masks thread just got locked up but man I've gotta give you massive props for this post... well done *applause*

 

[Buka]

A little movie music to take you into the weekend.....

 

[Steve]

I know this is somewhat political and I'm sorry for it. But I'm so sad for our country tonight. Just hearing from all of my friends and colleagues who are fellow veterans, many who are disabled in the line of duty. The feeling of betrayal is palpable. It's just been non stop tonight.

 

[drop bear]

 

[Buka]

I know this is somewhat political and I'm sorry for it. But I'm so sad for our country tonight. Just hearing from all of my friends and colleagues who are fellow veterans, many who are disabled in the line of duty. The feeling of betrayal is palpable. It's just been non stop tonight.

My heart goes out to you and your fellow veterans. And thank you. Sincerely, my brother.

I sometimes think the voices of support aren’t heard by those that served and protected all of us. Maybe folks take it for granted, maybe they don’t even realize it.

The fact that this is even a thing is so fricken wrong it kind of drives me crazy.

But, thanks, bro. Thanks to all who served. Thanks to all who protected me, mine and every single person I know.

We shall always salute you.

 

[granfire]

I know this is somewhat political and I'm sorry for it. But I'm so sad for our country tonight. Just hearing from all of my friends and colleagues who are fellow veterans, many who are disabled in the line of duty. The feeling of betrayal is palpable. It's just been non stop tonight.

It is tough to accept that those you sacrificed your health for are more interested in that truck you drove than how you can cope with life.

 

[Steve]

In about 8 or 9 more hours, that is going to be delicious.

 

[granfire]

em

In about 8 or 9 more hours, that is going to be delicious.

View attachment 23128

email a slice!

 

[granfire]

About a year ago, a young man who I knew causally at work, came up to me and said "I hear you're a guy who can get someone in shape". I said I was asked him what he needed.

He had just failed a fitness test for the FBI Academy- by one point. I said, "okay, we can do that, but we won't be going for one point, we'll be going to crush the fricken' thing. You game?" He was. We had three months. He wanted to know when we could start. I told him "Right now. And we don't do it the Law Enforcement way, we do it the Martial Arts way." I called his supervisor and said I needed him for twenty minutes, then called mine for a twenty minute relief.

Off we went to a storage area and started doing push ups, sit ups and pull ups. We did them every day at work, every day after work, every day when we were off. I did everything with him except the running - I don't run any more unless I'm chasing someone. I made him run while I yelled at him with a stopwatch in my hand.

God bless him, he showed up every day and worked his tail off. And he absolutely crushed that test, top of his class.

He graduated from the FBI Academy today. That's him on the left. Got me all teary eyed this morning.

View attachment 23118

I come to Hawaiier, and you can get me in shape.
Yesterday I discovered I own denim jeans (no stretchies!) and came to theobering conclusion that with my homebound lifestyle, I might not be able to button those up once the weather turns.
On the other hand, in Hawaii I could just ditch the jeans all together!
this fall will not be pretty!

 

[Buka]

I come to Hawaiier, and you can get me in shape.
Yesterday I discovered I own denim jeans (no stretchies!) and came to theobering conclusion that with my homebound lifestyle, I might not be able to button those up once the weather turns.
On the other hand, in Hawaii I could just ditch the jeans all together!
this fall will not be pretty!

It's very relaxed out here. You'll be fine.

 

[Monkey Turned Wolf]

I know this is somewhat political and I'm sorry for it. But I'm so sad for our country tonight. Just hearing from all of my friends and colleagues who are fellow veterans, many who are disabled in the line of duty. The feeling of betrayal is palpable. It's just been non stop tonight.

Been gone for a week, so out of the news cycle- is there any non-political way to tell me what happened?

 

[Steve]

Been gone for a week, so out of the news cycle- is there any non-political way to tell me what happened?

There was an article posted in the Atlantic that was pretty damning, and it has been corroborated by several other news outlets since it was published. The upshot is that there were comments made about people who service in the military being suckers and losers. I mean, it's nothing we didn't already know, but for whatever reason, this one seems to have done it for many veterans in a way that the bounties and the casual insults haven't yet. A Marine friend of mine, staunch Trump supporter who lives down the road from me with signs in his yard and flags on his car, conspicuously threw them all in the garbage. On that day, I was getting all kinds of texts and emails. The White House has been in damage control all weekend, so I don't know what sort of long term effect this might have. But I did see in the Military Times that, for the first time I can remember, a democrat has the lead by several points among active duty personnel, a swing of about 25% from 2016.

 

[Monkey Turned Wolf]

Man, I seriously F-ing miss sparring. More than just about anything else that I've lost from this quarantine. If I could do a 3 minute light-sparring kickboxing rules match with anyone experienced, I'd be happy.

Hell, I'm not a grappler, but if I could do a 3 minute roll with someone I'd be happy.

The funny thing is, I know people who would accomodate both of those but, living with my parents, I'm not willing. I can't wait for this whole thing to be over so I can get back to the fun part of MA.

 

[_Simon_]

Man, I seriously F-ing miss sparring. More than just about anything else that I've lost from this quarantine. If I could do a 3 minute light-sparring kickboxing rules match with anyone experienced, I'd be happy.

Hell, I'm not a grappler, but if I could do a 3 minute roll with someone I'd be happy.

The funny thing is, I know people who would accomodate both of those but, living with my parents, I'm not willing. I can't wait for this whole thing to be over so I can get back to the fun part of MA.

Oh brother I was literally thinking the same thing today!!! I'd give anything to spar... miss it greatly

 

[jks9199]

Been thinking about things.

I've decided that they're right.

Black flies DO splatter.

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