The most counterintuitive result ever!!!!

[DarkBlack]

Even if you are math-phobic, you should be able to answer this question.

Suppose you sum all the positive integers from 1 through infinity (1+2+3+............... ).

The answer is a really, really, really, really big number, right?

Well, no. I still haven't wrapped my mind around the idea, but the answer is -1/12.:confused2::confused2::confused2:

The proof is here:

[video]http://www.numberphile.com/videos/analytical_continuation1.html[/video]

Steve

I don't get the awe, or confusion. You said the sum of positive integers.
The first example the guy does in the video is put +1 -1 +2 -2...etc...

 

[smstonypoint]

I don't get the awe, or confusion. You said the sum of positive integers.
The first example the guy does in the video is put +1 -1 +2 -2...etc...

You need to watch the video a second time. Wear your glasses this time.

Steve

 

[DarkBlack]

You need to watch the video a second time. Wear your glasses this time.

Steve

watched it again. @ 1:20 into it, he's summing -1, -2 etc. Those are negative #'s not positive #'s, unless math has changed since I was in school.

 

[smstonypoint]

watched it again. @ 1:20 into it, he's summing -1, -2 etc. Those are negative #'s not positive #'s, unless math has changed since I was in school.

The initial question is what is the sum of all the positive integers from 1 through infinity (1+2+3+............... ).

The (informal) proof involves additional steps including multiplication, subtraction, etc.

Steve

 

[timswi]

Says someone who has never looked at an economics or finance journal (e.g.,Econometrica, American Economic Review, Review of Economics and Statistics, Journal of Finance, etc.). Accounting is arithmetic.

Steve

Accounting and Economics are different animals to be sure as are the calculations I utilize in SAS programs to begin the analysis process.

 

[smstonypoint]

Accounting and Economics are different animals to be sure as are the calculations I utilize in SAS programs to begin the analysis process.

I apologize for this in advance.

So, you are a "PROC - tologist."

Steve

PS -- I'm getting old. I think the first SAS manual I owned was well short of 200 pages in length.

 

[timswi]

I apologize for this in advance.

So, you are a "PROC - tologist."

Steve

PS -- I'm getting old. I think the first SAS manual I owned was well short of 200 pages in length.

I suppose you could say that--Sometimes it feels that way too....Truly amazing what that software is capable of, I doubt anyone on the planet knows everything it can do..Dr Goodnight et.al. created a masterpiece.

 

[Dr_Zinj]

Even if you are math-phobic, you should be able to answer this question.

Suppose you sum all the positive integers from 1 through infinity (1+2+3+............... ).

The answer is a really, really, really, really big number, right?

Well, no. I still haven't wrapped my mind around the idea, but the answer is -1/12.:confused2::confused2::confused2:

The proof is here:

[video]http://www.numberphile.com/videos/analytical_continuation1.html[/video]

Steve

Only if you work in the Congressional Budget Office, the IRS, or the Fed.

 

[Marveltone]

I've found that many theories don't hold water in the real world. For that, you need a bucket. I can hold a bucket and it can hold water. Theory makes my critters thirsty and my brain hurt.

Joe

 

[RedNeckRacin]

I think that string theory has evolved into plane theory for anyone who is interested. That stuff is so far out there that it twists the mind. Mr. Hawking is pretty dam impressive what he comes up with in his mind and I'm always fascinated when I read anything he writes about. Look into the theory about black holes. That gets into some trippy math as well!!