Talk:Even and odd functions: Difference between revisions

Revision as of 18:33, 12 May 2012

Revision as of 18:33, 12 May 2012

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<math>\chi_0:[-1,1] \to \{0,1\}</math> given by <math>\chi (0) = 1</math> and <math>\chi(x)=0, x \neq 0</math>

then, for <math>x \neq 0</math> we have <math>\chi(x)=0=\chi(-x)</math> and, for <math>x=0</math> , <math>\chi(-x)=\chi(0)=0=-0=-\chi(0)</math>

However I do believe that the only real functions which are both odd and even are real multiples of the characteristic function of <math>\{0\}</math>. --[[Special:Contributions/2.26.58.197|2.26.58.197]] ([[User talk:2.26.58.197|talk]]) 18:33, 12 May 2012 (UTC)