- Infinite sets
- rational numbers are countable
- real numbers are uncountable
- Cartesian product of sets
- cardinality of a Cartesian product
- fundamental counting principle
2.4 Essential Ideas
Two sets A and B are said to be in a one-to-one correspondence if we can find a pairing so that: (1) Each element of A is paired with precisely one element of B ; and (2) Each element of B is paired with precisely one element of A.
Finite and Infinite
A set is infinite if it can be placed in a one-to-one correspondence with a proper subset of itself. A set is finite if it is not infinite.
Fundamental Counting Principle
If task A can be performed in m ways, and after task A is performed, a second task B can be performed in n different ways, then the fundamental counting principle is that task A followed by task B can be performed in mn different ways.