# Thread: Countability - Finite Set

1. ## Countability - Finite Set

There is a statement in my book -

"a proper subset of a finite set and the finite set itself - can't have same cardinality"

Just wanted to check with you guys - To prove this we have to use Pigeon-Hole Principle. Correct? There is no way out without assuming that.

A yes/no would be good enough. (I know how to do the proof with Pigeon-Hole Principle)
Thanks

2. Originally Posted by aman_cc
There is a statement in my book -

"a proper subset of a finite set and the finite set itself - can't have same cardinality"

Just wanted to check with you guys - To prove this we have to use Pigeon-Hole Principle. Correct? There is no way out without assuming that.

A yes/no would be good enough. (I know how to do the proof with Pigeon-Hole Principle)
Thanks

Yes, though right now out of the blue I can't be 100% sure whether this is the UNIQUE way to prove it.

Tonio

3. Originally Posted by tonio
Yes, though right now out of the blue I can't be 100% sure whether this is the UNIQUE way to prove it.

Tonio
Thanks Tonio. It would definitely be interesting, though, to know if there are other ways to do it.