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Meaning of Notation.

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I am struggling with the notation/language of math.

1. What does f: Z----> Z or f: A--->A or f: N--->N mean? Are these the set of integers, natural numbers or any set in general (it is not the complex set)?

2. If I have:
Let A = {n:n>2} f: A--->A followed by some function does this mean A is a set of n integers?

Please give a clear, simple, explanation with some simple examples if possible.

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This solution explains the meaning of notations.

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