Partial function periodic

[Loki123]

I don't get this. Can someone explain. Correct is d. Why? I thought it was period 1 since it goes between 1 and 0.

 

[blamocur]

Function's image, a.k.a. range, is irrelevant to its periodicity. E.g., if [imath]f[/imath] were defined as being 5 for rational and 17 for irrational then the answer to the problem would be the same.

Can you provide the definitions from your class for a) periodic function, and b) function's period ?

 

[Loki123]

Function's image, a.k.a. range, is irrelevant to its periodicity. E.g., if [imath]f[/imath] were defined as being 5 for rational and 17 for irrational then the answer to the problem would be the same.

Can you provide the definitions from your class for a) periodic function, and b) function's period ?

I don't have it unfortunately. This is not a part of the class. I am trying to learn it on my own.

 

[blamocur]

Where did you get the problem from?

If you look at https://en.wikipedia.org/wiki/Periodic_function, they distinguish "a period", of which there can be many, and "the fundamental period". I am guessing your question is about the latter.

 

[JeffM]

The correct answer depends on the EXACT definition of periodic used by whoever posed the problem. Using the first paragraph of the Wikipedia definition cited above, this Dirichlet function is not periodic because it has no constant period. However, if you look up the Dirichlet function on Wikipedia, it says it is periodic. Everything depends on what definition you use.

 

[Loki123]

The correct answer depends on the EXACT definition of periodic used by whoever posed the problem. Using the first paragraph of the Wikipedia definition cited above, this Dirichlet function is not periodic because it has no constant period. However, if you look up the Dirichlet function on Wikipedia, it says it is periodic. Everything depends on what definition you use.

I am unfamiliar with the terms. I know the answer is d. What definition does that fit?

 

[blamocur]

I am unfamiliar with the terms. I know the answer is d. What definition does that fit?

I don't think it is productive to try solving the problem without understanding the definitions. And when there is more than one definition I would pick one and solve the problem for it.

 

[Loki123]

I don't think it is productive to try solving the problem without understanding the definitions. And when there is more than one definition I would pick one and solve the problem for it.

but i do not know the definitions, and while i can look them up, they don't give a clear idea on how to solve this problem.

 

[blamocur]

but i do not know the definitions, and while i can look them up, they don't give a clear idea on how to solve this problem.

You should look them up, and in case of ambiguity be clear in your post which definition you are using.
It would be very convenient if definitions gave us clear ideas about solutions, but, unfortunately, they rarely do.