If A is an infinite set, prove that A contains a subset of size n for any n>=1.
anyone can provide some hints for starting the proof?
Some authors say a set infinite if it is not finite.
Others say a set infinite if it is equipotent to a proper subset of itself.
Still others require an infinite set to contain a copy of the natural numbers.
While any of these lead to the same set of theorems and problems, the definition you are given it makes an enormous difference in the way one writes up a solution.
So how does your textbook/instructor define infinite set?