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Mathematics: This Will Blow Your Mind

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marshall
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01 Feb 2016, 10:03 pm

The series 1+2+3+... doesn't converge by definition. You can create an equivalence class between infinite series and values of the extended Riemann zeta function, but you should use "~" rather than "=". Write 1+2+3+4+... ~ -1/12, NOT 1+2+3+4+... = -1/12. Using the normal equals sign is a false equivocation because you're changing the definition of the equal sign.



Last edited by marshall on 01 Feb 2016, 10:09 pm, edited 1 time in total.

Deltaville
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01 Feb 2016, 10:07 pm

marshall wrote:
The series 1+2+3+... doesn't converge by definition. You can create an equivalence class between infinite series and values of the extended Riemann zeta function, but you should use "~" rather than "=". Write 1+2+3+4+... ~ -1/12, NOT 1+2+3+4+... = -12. Using the normal equals sign is a false equivocation because you're changing the definition of the equal sign.



Correct. More or less, the answer is dependent on gamma. The RZF is really useless however, electrical engineering is the only discipline that uses it, I think.


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Deltaville
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01 Feb 2016, 10:13 pm

marshall wrote:
The series 1+2+3+... doesn't converge by definition. You can create an equivalence class between infinite series and values of the extended Riemann zeta function, but you should use "~" rather than "=". Write 1+2+3+4+... ~ -1/12, NOT 1+2+3+4+... = -1/12. Using the normal equals sign is a false equivocation because you're changing the definition of the equal sign.


True! In fact the the proper answer would be -1/12, if lim-> x extends to infinity, and a complex value operator is present, other wise we assume X is an element of real numbers.


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