Talk:Even and odd functions

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Field: Analysis

Extensions?

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 $f : G \to H$, where $(G,+)$ and $(H,+)$ are arbitrary groups. Thus it also works without any change for vector spaces of any dimension. --131.188.3.21 (talk) 11:47, 16 June 2009 (UTC)

Origin

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. 216.167.142.196 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.

Why?

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. 69.143.236.33 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.--86.165.254.170 (talk) 16:08, 6 May 2008 (UTC)

Negative exponents

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)

Proofs

The proprieties listed here http://en.wikipedia.org/wiki/Even_and_odd_functions#Basic_properties 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)

Definitions

I think we should make the definitions of odd and even functions more strict. My suggestions are:
Let $f:A\to\mathbb{R}$ where $A\subseteq\mathbb{R}$ ƒ is even if and only if $f(x)=f(-x)$ for all $x\in A$
Similarily ƒ is odd if and only if $f(x)=-f(-x)$ for all $x\in A$
DanielEriksson87 15:06, 11 September 2007 (UTC)

real-valued

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. --131.188.56.77 (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)