MHB Give an example of a function ....

[alexmahone]

Give an example of a function which is periodic, non-constant, and yet has no minimal period.

 

[Evgeny.Makarov]

Read the Wikipedia article on periodic functions.

 

[alexmahone]

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]

But it gives an example you are looking for in the last paragraph of the Examples section.

 

[alexmahone]

But it gives an example you are looking for in the last paragraph of the Examples section.

Thanks.

 

[HallsofIvy]

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.