Is Non-Periodicity Impossible in Functions?

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A function is defined as periodic if f(x + P) = f(x) for all x. If a function is not periodic, it does not mean that f(x + P) = f(x) is impossible; rather, it indicates that there are some values of x for which this equation does not hold. However, there can still be many values of x where f(x + P) equals f(x). Therefore, non-periodicity does not negate the existence of specific instances of periodicity within a function. The discussion clarifies the nuances of periodic and non-periodic functions.
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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