- #1
Bipolarity
- 776
- 2
Can a function have two periods? If so, which is the fundamental period?
Consider the following function, $$ f : \mathbb{N} → \mathbb{R} $$, defined by
f[n] = 1 if n is a multiple of 2 or 3, and 0 otherwise.
Then it is clear that 2 and 3 are both periods of this function, since translation of the input by either 2 or 3 renders the function's value invariant.
6, being the least common multiple of 2 and 3, is also "a period" of this function. But which is the fundamental period?
Thanks to anyone who can clarify this confusion!
BiP
Consider the following function, $$ f : \mathbb{N} → \mathbb{R} $$, defined by
f[n] = 1 if n is a multiple of 2 or 3, and 0 otherwise.
Then it is clear that 2 and 3 are both periods of this function, since translation of the input by either 2 or 3 renders the function's value invariant.
6, being the least common multiple of 2 and 3, is also "a period" of this function. But which is the fundamental period?
Thanks to anyone who can clarify this confusion!
BiP