- #1
Wiz14
- 20
- 0
1.There exists an injection from A to B ⇔ A ≤ B
2.There exists an injection from B to A ⇔ B ≤ A
3.If A ≤ B and B ≤ A, then A = B
Does this prove the Cantor Bernstein theorem? Which says that if 1 and 2 then there exists a Bijection between A and B (A = B)
And if it does, why is there a different, longer proof for it?
2.There exists an injection from B to A ⇔ B ≤ A
3.If A ≤ B and B ≤ A, then A = B
Does this prove the Cantor Bernstein theorem? Which says that if 1 and 2 then there exists a Bijection between A and B (A = B)
And if it does, why is there a different, longer proof for it?