I love numbers as much as I love words.

http://www.numberphile.com/vid...l_continuation1.html

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

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.

As a non-mathematician, I thought the figure they arrived at was an average.

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, January 18, 2014 20:35

I'll take your word for it.

What was the serious flaw?

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.

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.

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.

quote:

Don't make the mistake of thinking that mathematics starts and ends with arithmetic.

Bob, can you explain that?

Nice link, goofy.

arithmetic = add subtract multiply or divide real numbers

other branches of mathematics include

complex numbers
geometry - Euclidean and non-Euclidean
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, January 23, 2014 02:48

quote:

and so on and so forth... arithmetic is (usually) just adding stuff up.

And the rest is just making things up?

I thought so, but I wanted to be sure. In that link that goofy provided, many of the comments were about arithmetic.

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.

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