Give an example of a function ....

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The discussion centers on identifying a periodic, non-constant function that lacks a minimal period. A specific example provided is the function defined by f(x) = 0 for x = 1 and f(x+y) = f(x) + f(y) for all x and y, which is periodic with every rational number serving as a period. This function is non-continuous and exemplifies the characteristics outlined in the Wikipedia article on periodic functions.

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Give an example of a function which is periodic, non-constant, and yet has no minimal period.
 
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Read the Wikipedia article on periodic functions.
 
Evgeny.Makarov said:
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.
 
But it gives an example you are looking for in the last paragraph of the Examples section.
 
Evgeny.Makarov said:
But it gives an example you are looking for in the last paragraph of the Examples section.

Thanks.
 
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.
 

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