# Cardinality of sets (1 Viewer)

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

#### Focus

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

#### 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.

#### Preno

It's an infinite sequence of natural numbers.

#### AKG

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

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

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