-3

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

I can't really tell what is obviously wrong with this. It seems to use the same logic as we see in the derivation of things like $\sum_{k=1}^{\infty} k = -\frac{1}{12}$ which appears to be a quirky but accepted fact in mathematics.

Praveen
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AureliusPhi
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1 Answers1

3

The third line, what does $$1 - 1 + 1 - 1 + 1 - 1 + \cdots$$

mean? It's certainly not a convergent series like lines one, two, four and five.

Simon S
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  • It's the second line, minus the parentheses – AureliusPhi Nov 03 '14 at 21:24
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    Yes, but whenever we have an infinite sum in mathematics we have to know that it actually exists. Just because we can write something down with marks on the page or the screen doesn't mean it makes sense. – Simon S Nov 03 '14 at 21:29