sum of all integers

why isn't it the case that the sum of all integers is 0?

1+(-1)+2+(-2)+3+(-3)...n+(-n)=0+0+0...+0=0

is it just because you can't apply the regular rules for arithmetic to infinite sums?

Because "infinite sums" aren't defined in the way you'd expect. An infinite sum is defined to be equal to a fixed A if the limit of the sequence of partial sums is A. Any arithmetic rules that you see being used in math textbooks or that you learn in school are just consequences of the actual definition. This does not mean that all normal arithmetic rules work.

>>1
Because it doesn't converge. It's never getting closer to zero, it's oscillating around it, and only convergent series have a limit as they tend to infinity.

http://en.wikipedia.org/wiki/Convergent_series

>>1
Because there are no negative numbers.

sum(n=1..inf, -n+n) = 0

>>4
in after troll

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Marijuana MUST be legalized.