Difference between revisions of "Talk:Period of a function"
From Encyclopedia of Mathematics
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==Minimal period== | ==Minimal period== | ||
The article states "If a real-valued function $f$ of a real argument is periodic on $X$ (and is not identically equal to a constant), then it has a least period $T_0>0$". And yet the Dirichlet function $D(x)$, presented two sentences earlier, has no such minimum period. Presumably some extra condition is missing? [[User:Richard Pinch|Richard Pinch]] ([[User talk:Richard Pinch|talk]]) 23:06, 20 October 2017 (CEST) | The article states "If a real-valued function $f$ of a real argument is periodic on $X$ (and is not identically equal to a constant), then it has a least period $T_0>0$". And yet the Dirichlet function $D(x)$, presented two sentences earlier, has no such minimum period. Presumably some extra condition is missing? [[User:Richard Pinch|Richard Pinch]] ([[User talk:Richard Pinch|talk]]) 23:06, 20 October 2017 (CEST) | ||
| + | :How ridiculous: a statement follows its counterexample... Well, [https://dic.academic.ru/dic.nsf/enc_mathematics/3932/%D0%9F%D0%95%D0%A0%D0%98%D0%9E%D0%94 the Russian version] contains the adjective "continuous" (but "periodic" is missing there). I'll add "continuos" here. [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 09:28, 21 October 2017 (CEST) | ||
Latest revision as of 07:28, 21 October 2017
Minimal period
The article states "If a real-valued function $f$ of a real argument is periodic on $X$ (and is not identically equal to a constant), then it has a least period $T_0>0$". And yet the Dirichlet function $D(x)$, presented two sentences earlier, has no such minimum period. Presumably some extra condition is missing? Richard Pinch (talk) 23:06, 20 October 2017 (CEST)
- How ridiculous: a statement follows its counterexample... Well, the Russian version contains the adjective "continuous" (but "periodic" is missing there). I'll add "continuos" here. Boris Tsirelson (talk) 09:28, 21 October 2017 (CEST)
How to Cite This Entry:
Period of a function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Period_of_a_function&oldid=42144
Period of a function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Period_of_a_function&oldid=42144