Cardinality of Sets: N & Omega Explained

[saadsarfraz]

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]

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

 

[saadsarfraz]

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]

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]

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

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