9 ms·
Your error is here, equality is wrong: -1 + 1 - 1 + 1 - 1 ... = (-1 + 1) + (-1 + 1) ... In first series, there are 2 different elements (1 and -1) and series
by cLeEOGPw 10y ago
Your error is here, equality is wrong: -1 + 1 - 1 + 1 - 1 ... = (-1 + 1) + (-1 + 1) ...
In first series, there are 2 different elements (1 and -1) and series can end at any one of them rendering the end result of the sum uncertain. On second one there is only one element - (-1 + 1) which is 0, so wherever you end it the result is always the same.
- ebola1717 10y agoMy whole point was there are operations that work in finite mathematics that don't work on infinite series, so yes, I didn't prove mathematics inconsistent, I just proved grouping is illegal for divergent infinite series :) To be clear, yes (1 - 1) + (1 - 1) + ... != 0 + 0 + ... either
- cLeEOGPw 10y ago> To be clear, yes > (1 - 1) + (1 - 1) + ... != 0 + 0 + ... either I don't see why. I understand the sets themselves are not equal, but the sum of the elements of those sets is at any given index.
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