Aleph-zero

The set theory symbol \(\aleph_0\) (aleph-zero) refers to a set the same cardinal number as the "small" infinite set of integers.
It is also sometimes pronounced as "aleph-zero", "aleph-null” or "aleph-naught", the latter of which is also spelled "aleph-nought".
The algebraic numbers also have cardinality \(\aleph_0\). Properties satisfied by \(\aleph_0\) include:
\(\aleph_0^r=\aleph_0\) for \(r>0\) 
\(r\,\aleph_0=\aleph_0\) for \(r\neq0\)
\(\aleph_0+f=\aleph_0\)
where \(f\) is any finite set. However:
\(2^{\aleph_0}={\aleph_1}=c\)
where \(c\) is the continuum.
== Sources ==
# https://mathworld.wolfram.com/Aleph-0.html
Category:Aleph numbers
Category:Transfinite ordinals