# Cardinality of sets

1. Mar 16, 2009

The cardinality of set of [N]$$\omega$$ . what does omega stands for?

2. Mar 17, 2009

### Focus

This seems a bit out of the blue, I never seen something like that but could it by any chance be referring to $X^Y=\{f : Y \rightarrow X \}$ ?

3. Mar 17, 2009

### matt grime

The lower case omega is (usually) the first infinite ordinal.

4. Mar 17, 2009

so is omega the same as aleph not. and in this case it would be aleph not to the power aleph not which gives aleph not?

5. Mar 18, 2009

### CRGreathouse

omega's cardinality is aleph naught. But omega is an ordinal, while aleph naught is a cardinal.

6. Mar 18, 2009

### Preno

It's an infinite sequence of natural numbers.

7. Mar 18, 2009

### AKG

Usually the notation $[N]^{\omega}$ denotes the collection of subsets of N of size $\omega$, i.e.:

$$[N]^{\omega} = \{ X \subseteq N : |X| = \omega \}$$