Some Facts
A function's being odd or even does not imply differentiability, or even continuity. For example, the Dirichlet function is even, but is nowhere continuous. Properties involving Fourier series, Taylor series, derivatives and so on may only be used when they can be assumed to exist.
Read more about this topic: Even And Odd Functions
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“All the facts of nature are nouns of the intellect, and make the grammar of the eternal language. Every word has a double, treble or centuple use and meaning.”
—Ralph Waldo Emerson (1803–1882)
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