Thread: cardinal numbers! proof

1)Prove that binary relation ≤ is antisymmetric in the set of the cardinal numbers.

2)Prove that binary relation ≤ is transitive in the set of the cardinal numbers.
can u guys help me?

should i prove first one with cantor-bernstein theorem? just prove cantor-bernstein and is that all? or what? (

1) if k ≤ m is defined as "there exists an injection from any set A with |A| = k to any set B with |B| = m" then (1) IS cantor-bernstein.

2) show that the composition of two injective maps is injective.