# Cardinality of sets

## Main Question or Discussion Point

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

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

matt grime
Homework Helper
The lower case omega is (usually) the first infinite ordinal.

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?

CRGreathouse
Homework Helper
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?
omega's cardinality is aleph naught. But omega is an ordinal, while aleph naught is a cardinal.

It's an infinite sequence of natural numbers.

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