Do All Uncountable Sets Share the Same Cardinality?

[sphelan08]

Mathmatical proofs help please!

1. Must two uncountable sets have the same cardinality?
a countable union of countable sets is countable.
Is a finite set necessarily countable?
If the union of A and B is infinite, then A or B must be inifinte



2. Just use definitions of Uncountable, Countable, finite, and infinite, and cardinality to do these proofs.


3. I know what the answers are just by thinking but I cannot prove the answers please help or I will fail

 

[Dick]

Well, state the definitions, then state what you are thinking and try to use the definitions to prove what you thinking. You have to give us something to go on.

 

[hunt_mat]

The cardinality of a finite set is just the number of elements of that set.