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## Homework Statement

Check the title

## Homework Equations

Using the following definition of finite/infinite:

A set X is infinite iff [itex]\exists f:X \rightarrow X[/itex] that is injective but [itex]f(X) \not= X[/itex], i.e. [itex]f(X) \subset X[/itex].

A set X is finite iff [itex]\forall f:X \stackrel{1-1}{\rightarrow} X[/itex] it must follow that [itex]f(X) = X[/itex].

## The Attempt at a Solution

My instructor's very picky about the definitions I'm supposed to use, but I'm having a lot of trouble wrapping my head around this. Could someone explain them to me? And what information I'm supposed to get from the definition?

Thanks in advance.