Talk:Even and odd functions

From Wikipedia, the free encyclopedia
Jump to: navigation, search
WikiProject Mathematics (Rated C-class, High-importance)
WikiProject Mathematics
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
C Class
High Importance
 Field: Analysis


are there extensions of these simple idas to higher dimensions? --achab 16:44, 28 May 2007 (UTC)

This concept is in no way bound to real numbers. The definition can be applied verbatim to any function , where and are arbitrary groups. Thus it also works without any change for vector spaces of any dimension. -- (talk) 11:47, 16 June 2009 (UTC)


Okay, so what *is* the original of the terms even/odd, if not from Taylor series? It's certainly not just "coincidence", as no sane person would keep the term "odd" for the even-powered monomials or vice versa. 04:46, 17 November 2005 (UTC)

Originally, the word "even" comes from "level", while "odd" comes from "sticking out". [1] says that the first instance of "even function" was in 1727 by Leonhard Euler, "odd function" in 1819 ([2]). — Omegatron 21:56, 17 January 2007 (UTC)

Starting with quotients, there is a word missing in the properties.


The choice of even and odd seems arbitrary, I've never seen it explained anywhere. Could somebody explain the motivation for defining even and odd functions? --yoshi 05:32, 23 January 2006 (UTC)

Even when you divide in half you have mirror image on each side of divisor (so it equals itself). Odd you're one man short which makes people sad. To signify sadness/negativity, we use the minus sign. 06:29, 12 October 2007 (UTC)
As far as I'm aware, the terms odd and even are derived from the exponents of some basic odd and even functions ; x2 has the property that f(x)=f(-x) -- i.e. x2=(-x)2. Similarly with x4, x6 and so on. Since these have even exponents, all other functions which have this property are referred to as even. The opposite is true for x, x3, x5 and so on, so they are referred to as odd functions.-- (talk) 16:08, 6 May 2008 (UTC)

Negative exponents[edit]

So is xn an odd function if n is a negative odd integer (even if it's undefined at zero)? — Loadmaster 20:03, 17 January 2007 (UTC)

Yes. --Spoon! 03:33, 13 March 2007 (UTC)


The proprieties listed here are quite plain.. Somoene should add a short proof for each propriety.—Preceding unsigned comment added by stdazi (talkcontribs)

I'm not sure that's a good idea. The properties are so simple, I think the proofs can be left to the reader. Perhaps a proof or two could be given, but we don't need one for every property. Doctormatt 23:07, 11 August 2007 (UTC)


I think we should make the definitions of odd and even functions more strict. My suggestions are:
Let where ƒ is even if and only if for all
Similarily ƒ is odd if and only if for all
DanielEriksson87 15:06, 11 September 2007 (UTC)


The definition in the article restricts f to be real valued. There is no need for this restriction. Actually it is often usefull to also consider complex valued even or odd functions. -- (talk) 09:16, 16 June 2009 (UTC)

I think for Complex function you have to use the conjugate.--Royi A (talk) 20:12, 24 September 2009 (UTC)

Geometric properties?[edit]

A graph of an even function has reflection symmetry, and a graph of an odd number has rotation symmetry. (talk) 00:41, 10 May 2015 (UTC)

أسامة حسن حسين[edit]

أسامة حسن حسين هو طالب في مدرسة (ٍStem).يقال أن السيد أسامة هو اكثر شخص اكتأبا ولكن أنا أنفي ذلك نفي بات. — Preceding unsigned comment added by (talk) 17:34, 8 December 2016 (UTC)