Is Non-Periodicity Impossible in Functions?

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SUMMARY

The discussion centers on the concept of periodic functions in mathematics, specifically addressing the equation f(x + P) = f(x). It is established that if this equation holds for all x, the function is periodic. However, the participants clarify that a function can be non-periodic while still satisfying the equation for certain values of x, indicating that non-periodicity does not universally negate the possibility of the equation being true for specific instances.

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Fabio010
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Ok as we know, if f(x+P) = f(x) then the function is periodic.

So if the function is not periodic, f(x+p) = f(x) is a impossible equation right?
 
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Fabio010 said:
Ok as we know, if f(x+P) = f(x) then the function is periodic.

So if the function is not periodic, f(x+p) = f(x) is a impossible equation right?

Nope. You forgot something in your first sentence about periodicity...
 
If f(x+ p)= f(x) for all x then f is periodic. If f is NOT periodic, then there exist some x f(x+ p) is not the same as f(x). But there still might be many x for which that is true.
 

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