Cardinality Flashcards
1
Q
Same cardinality
A
There is a bijection A—>B or B—>A
2
Q
|A|<=|B|
A
Injection A—>B
3
Q
|A|<|B|
A
No onto function A—>B
4
Q
Countable
A
A set that is finite or has the same cardinality as the set of natural numbers
5
Q
|N|
A
Aleph null
6
Q
Schroeder-Bernstein Theorem
A
if |A|<=|B| & |B|<=|A|, then |A|=|B|
7
Q
Continuum
A
Cardinality of Real numbers
|R|=Aleph
8
Q
Cantor’s Theorem
A
If f: A—>2^A, then f is not onto
9
Q
Cantor-Bernstein-Schroeder Theorem
A
|R|=2^|N|, or Aleph=2^(Aleph null)
