Editing Limit cardinal (section)

{{Short description|Class of cardinal numbers}}
In [[mathematics]], '''limit cardinals''' are certain [[cardinal number]]s. A cardinal number ''λ'' is a '''weak limit cardinal''' if  ''λ'' is neither a [[successor cardinal]] nor zero. This means that one cannot "reach" ''λ'' from another cardinal by repeated successor operations. These cardinals are sometimes called simply "limit cardinals" when the context is clear.

A cardinal ''λ'' is a '''strong limit cardinal''' if ''λ'' cannot be reached by repeated [[Power set|powerset]] operations. This means that ''λ'' is nonzero and, for all ''κ'' < ''λ'', 2<sup>''κ''</sup> < ''λ''. Every strong limit cardinal is also a weak limit cardinal, because ''κ''<sup>+</sup> ≤ 2<sup>''κ''</sup> for every cardinal ''κ'', where ''κ''<sup>+</sup> denotes the successor cardinal of ''κ''.

The first infinite cardinal, <math>\aleph_0</math> ([[Aleph number#Aleph-nought|aleph-naught]]), is a strong limit cardinal, and hence also a weak limit cardinal.