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I love numbers as much as I love words. http://www.numberphile.com/vid...l_continuation1.html "No man but a blockhead ever wrote except for money." Samuel Johnson.  

Member 
That's sum conclusion! I had heretofore thought it was 42.  

Member 
There is of course a serious flaw in what they are doing but apparently the value =1/12 can be assigned to the set by rather more rigorous mathematics. "No man but a blockhead ever wrote except for money." Samuel Johnson.  

<Proofreader> 
As a nonmathematician, I thought the figure they arrived at was an average.  
Member 
It wasn't anything... you can't perform arithmetic or algebraic functions on diverging series. It's as simple as that. The operations are undefined. It's still a cute trick though.This message has been edited. Last edited by: BobHale, "No man but a blockhead ever wrote except for money." Samuel Johnson.  

<Proofreader> 
I'll take your word for it.  
Member 
What was the serious flaw?  

Member 
It was. The serious flaw is that you just aren't allowed to do those operations on that kind of object. It makes as much mathematical sense as saying an apple plus an orange equals a banana. "No man but a blockhead ever wrote except for money." Samuel Johnson.  

Member 
I didn't understand it at all. Infinity is not a real number, but rather a concept meaning limitless. Infinity has no beginning and no end, so I don't see how 1+2+3+4+5+6...∞ can be given a value. From what I recall, 1+2+3+4+5+6...n =(n+1)(n/2) = n(n+1)/2 = (n^2+n)/2, where n is a real number. But when n=∞ the formula doesn't work. I'm lost.  

Member 
Because you don't understand series. 1 + 1/2 + 1/4 + 1/8 + 1/16... is also an infinite series, the terms go on forever but the limit of the series is 2. You go on adding terms forever getting closer and closer to 2. On this kind of series it's legitimate to say that the sum from 0 to infinity is 2. You can perform matheematical operations on this type of series (converging) The square roots of negative numbers are also "meaningless" in the sense that infinity is but without them whole swathes of mathematics can't work. Don't make the mistake of thinking that mathematics starts and ends with arithmetic. "No man but a blockhead ever wrote except for money." Samuel Johnson.  

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Bob, can you explain that? Nice link, goofy.  

Member 
arithmetic = add subtract multiply or divide real numbers other branches of mathematics include complex numbers geometry  Euclidean and nonEuclidean calculus  differential and integral algebra set theory number theory topology probability statistics chaos theory game theory trigonometry and so on and so forth... arithmetic is (usually) just adding stuff up.This message has been edited. Last edited by: BobHale, "No man but a blockhead ever wrote except for money." Samuel Johnson.  

<Proofreader> 
And the rest is just making things up?  
Member 
I thought so, but I wanted to be sure. In that link that goofy provided, many of the comments were about arithmetic.  

Member 
Most of the "proof" in the video is simple arithmetic but that's exactly the problem  you can't do arithmetic on diverging series. It doesn't work. "No man but a blockhead ever wrote except for money." Samuel Johnson.  

Member 
Interesting, when I looked up mathematics compared to arithmetic, I found that the mathematical sciences used to include geometry, astronomy and optics.  

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