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Quick math question

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An interesting related mathematics conundrum...

0 = 0
0 = 0 + 0 + 0 + 0 + 0 + 0 + ...
0 = (1 - 1) + (1 - 1) + (1 - 1) + (1 - 1) + ...
0 = 1 + (-1 + 1) + (-1 + 1) + (-1 + 1) + ...
0 = 1

How is this possible? The solution (as to why this isn''t true) is found in the study of infinite series.

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That doesn't require the study of infinite series to solve. The answer is that you're assuming that 1 - 1 + 1 - 1 + 1 - 1 + ... actually equals something, which it obviously does not.

Try this one:

"proof" that everything = everything

Let a be a number greater than b, and let c be the difference.

a = b + c
a(a - b) = (b + c)(a - b)
a2 - ab = ab + ac - b2 - bc
a2 - ab - ac = ab - b2 - bc
a(a - b - c) = b(a - b - c)
a = b

[edited by - Beer Hunter on March 23, 2002 6:16:45 PM]

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Guest Anonymous Poster
(a-b-c) is 0. Just because x*0 = 0 and y*0 = 0 doesn''t imply x = y.

Enough with the algebra games. Do some useful math.

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quote:
Original post by Beer Hunter
That doesn''t require the study of infinite series to solve. The answer is that you''re assuming that 1 - 1 + 1 - 1 + 1 - 1 + ... actually equals something, which it obviously does not.


Actually, it does equal something. "Obviously", the series:

(sigma from n=0 to infinity) (1-1) = 0 and
(sigma from n=0 to infinity) (0) = 0.

If you add x sets of 0 together you get 0 and
If you add x sets of (1 - 1) together you get 0.

I would think you would at least know that before taking 2nd/3rd (?) semester calculus.

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quote:
Original post by mnansgar
Actually, it does equal something. "Obviously", the series:

(sigma from n=0 to infinity) (1-1) = 0 and
(sigma from n=0 to infinity) (0) = 0.


And since when infinity times 0 = 0 ?

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quote:
Original post by pouya
And since when infinity times 0 = 0 ?


A sigma sign means to add, not multiply, if that''s what you''re getting at ...

(sigma n=0 to infinity) (n) is equivalent to (0 + 1 + 2 + 3 + ...).
(sigma n=0 to infinity) (1) is equivalent to (1 + 1 + 1 + 1 + ...).

Sorry if I misunderstood.

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Oh okay, I thought you means the sum of all those n''s, times zero.
My bad.

(now if the damn slowass gamedev server would let me post this after the fifth time it timed out)

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I have to wonder at the whole point of this thread! Unless someone can justify to me its relevance to Game Programming, I will close this thread and spare us all these pointless posts filled with erroneous divide by zero errors and bi-modal infinite series!

Timkin

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