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Give an example of a function ...

Alexmahone

Active member
Jan 26, 2012
268
Give an example of a function which is periodic, non-constant, and yet has no minimal period.
 

Evgeny.Makarov

Well-known member
MHB Math Scholar
Jan 30, 2012
2,493
Read the Wikipedia article on periodic functions.
 

Alexmahone

Active member
Jan 26, 2012
268
Read the Wikipedia article on periodic functions.
I know what a periodic function is and I read the Wikipedia article. Yet, I cannot answer the question.
 

Evgeny.Makarov

Well-known member
MHB Math Scholar
Jan 30, 2012
2,493
But it gives an example you are looking for in the last paragraph of the Examples section.
 

Alexmahone

Active member
Jan 26, 2012
268

HallsofIvy

Well-known member
MHB Math Helper
Jan 29, 2012
1,151
Since you appear to already have the answer, let f(x) be any non-continuous function satisfying f(1)= 0 and f(x+y)= f(x)+ f(y). That will be periodic with every rational number as period.