Give an example of a function ....

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Discussion Overview

The discussion revolves around identifying a function that is periodic, non-constant, and lacks a minimal period. Participants explore definitions and examples related to periodic functions.

Discussion Character

  • Exploratory, Debate/contested, Conceptual clarification

Main Points Raised

  • One participant requests an example of a periodic function that is non-constant and has no minimal period.
  • Several participants suggest referring to the Wikipedia article on periodic functions for guidance.
  • A later reply proposes a specific function, defined as a non-continuous function satisfying f(1)= 0 and f(x+y)= f(x)+ f(y), claiming it is periodic with every rational number as a period.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the example of the function, and there are multiple references to external sources without a definitive answer being provided.

Contextual Notes

Some participants express familiarity with the concept of periodic functions but still struggle to provide an example, indicating potential limitations in understanding or application of the definitions.

alexmahone
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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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