Talk:Even and odd functions: Difference between revisions

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==Extensions?==
are there extensions of these simple idas to higher dimensions?
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==Integral of an odd function==
For an odd function <math>f(x)</math> the integral <math>\int_{-A}^{A} f(x) dx = 0</math> even when <math>A = \infty</math>. The statement that <math>A</math> must be finite is incorrect. My contribution to this paragraph has this citation, the original content appears to have no citation for to support its incorrect assertion.<ref>http://mathworld.wolfram.com/OddFunction.html</ref>
<ref>http://mathworld.wolfram.com/OddFunction.html</ref>
:{{ping|MathInclined}} This is not true. <math>\int_{-\infty}^{+\infty} x dx</math> does not even exist. If one wants to make sense of that, one must generally resort to [[Cauchy principal value]]s. This is not contradicted by the link you gave, which deals with bounded intervals only. The subtle point is the meaning of integrability over the whole real line.--[[User:Jasper Deng|Jasper Deng]] [[User talk:Jasper Deng|(talk)]] 07:45, 11 December 2017 (UTC)
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== Teddy theorem ==
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* Presented as it is, the theorem is wrong as supposing implicitely that all functions are infinitely differentiable. The way of preenting the result in the section "In calculus" is also confusing, but the title of the section lets the reader supposing that the functions considered are differentiable. However, it would be better to mention that in the section.
In summary, the edits add nothing else than unreliable references and a theorem name that is [[WP:OR]]. They cannot be accepted without breaking Wikipedia policies. [[User:D.Lazard|D.Lazard]] ([[User talk:D.Lazard|talk]]) 15:25, 7 November 2019 (UTC)
 
== I think the convention in definition is to put f(-x) to the left of the equal sign. ==
 
That's how it is in my textbooks and at Wolfram. [[Special:Contributions/69.5.112.154|69.5.112.154]] ([[User talk:69.5.112.154|talk]]) 23:36, 2 May 2023 (UTC)