Editing Hereditarily finite set (section)

==Discussion==
The set <math>\{\{\},\{\{\{\}\}\}\}</math> is an example for such a hereditarily finite set and so is the empty set <math>\{\}</math>, as noted. 
On the other hand, the sets <math>\{7, {\mathbb N}, \pi\}</math> or <math>\{3, \{{\mathbb N}\}\}</math> are examples of finite sets that are not ''hereditarily'' finite. For example, the first cannot be hereditarily finite since it contains at least one infinite set as an element, when <math>{\mathbb N} = \{0,1,2,\dots\}</math>.

The class of all hereditarily finite sets is denoted by <math>H_{\aleph_0}</math>, meaning that the cardinality of each member is smaller than <math>\aleph_0</math>. (Analogously, the class of [[hereditarily countable set|hereditarily ''countable'' set]]s is denoted by <math>H_{\aleph_1}</math>.)
<math>H_{\aleph_0}</math> is in bijective correspondence with <math>\aleph_0</math>.
It can also be denoted by <math>V_\omega</math>, which denotes the <math>\omega</math>th stage of the [[von Neumann universe]].<ref>{{cite web |url=https://ncatlab.org/nlab/show/hereditarily+finite+set |title=hereditarily finite set |author-link=nLab |date=January 2023 |website=nLab |access-date=January 28, 2023 |quote=The set of all (well-founded) hereditarily finite sets (which is infinite, and not hereditarily finite itself) is written <math>V_\omega</math> to show its place in the von Neumann hierarchy of pure sets.}}</ref>
So here it is a [[Countable set|countable]] set.