What is the total sum of all numbers?

[Baby Astronaut]

For every positive number there is a negative number and they form a pair whose sum is zero.

Wow, that made me think of a comparison to matter/antimatter.

 

For every positive matter there is negative matter and they form a pair whose sum is annihilation.

[minus_Ph]

Suppose [math]1+2+4+8+\cdots[/math] exists. Call this sum S:

 

[math]S\equiv\sum_{n=0}^{\infty}2^n[/math]

 

Multiply S by two:

 

[math]2S = 2\sum_{n=0}^{\infty}2^n = \sum_{n=0}^{\infty}2\cdot2^n = \sum_{n=0}^{\infty}2^{n+1} = \sum_{n=1}^{\infty}2^n[/math]

 

The last expression is just the original sum sans the zeroth element: [math]2S=S-1[/math] and thus [math]S=-1[/math].

 

See http://en.wikipedia.org/wiki/1_%2B_2_%2B_4_%2B_8_%2B_·_·_·

 

Which is just another proof that any number multiplied by infinity looses its identity...

Similar things happen to any matter that falls into a singularity.

The problem here is that few understand the ambiguation that happens when infinity is used.

The real answer to the original post is ANY NUMBER.

So 42 is just as valid as any other.

The truly tragic part of this is that I cannot pick lotto numbers by summing all numbers... I would win every time.

~minus

[cameron marical]

i think its the 0, since infinity isnt a real number, so far as we know. but then again, 0 iskind of an opinion number too, since it has no value.

 

no, i doubt it equals one, i really think that its zero, the sum of all numbers is zero. say n=all positive numbers, and N=all negative numbers, well n + N=0 then. only for the sum though, if its something like the dividend, then that might be a little harder, or maybe thats just 0 too.

[the tree]

i think its the 0, since infinity isnt a real number

Infinity isn't a number, period. Let alone a real one.

 

0 is a reasonable answer, but strictly speaking it's undefined.

 

Your approach is basically.

 

[math]\int_{-\infty}^{\infty}x \, dx = \int_{-\infty}^{0}x \, dx + \int_{0}^{\infty}x \, dx[/math]

 

Which is intuitively zero, but say you make another completely arbitrary split.

 

[math]\int_{-\infty}^{\infty}x \, dx = \int_{-\infty}^{0}x \, dx + \int_{0}^{14\frac{2}{3}}x \, dx + \int_{14\frac{2}{3}}^{\infty}x \, dx[/math]

 

Then by the same intuition, you get 14²/₃. See the problem?

 

no, i doubt it equals one

It doesn't, all those "equations" are sort of jokes. They're examples of the silly things that happen when you make unfounded assumptions like the existence of a limit. (although some of them turn out to be surprisingly applicable to the real world) Edited January 28, 2009 by the tree

[cameron marical]

oh, okay, i was wondering how people got 42, like of the hitchhikers guide to the galaxy.

 

although some of them turn out to be surprisingly applicable to the real world)

but, how are they applicable to the real world? im not really much of a mathmetician, engineering is more my kind of thing. and physics.

 

Then by the same intuition, you get 142/3. See the problem?

 

oh, ok, i do now see the problem. whats your best guess, Mr. The Tree?

[empty]

that remind me Laurent series

[Twerpy]

oh, ok, i do now see the problem. whats your best guess, Mr. The Tree?

 

The set of all numbers?

[the tree]

I'm sticking with it being undefined kthx.