Editing Internal set theory (section)

==== Applied to the relation ∈ ====
We take {{tmath|R(g, f)}}: ''g'' is a finite set containing element ''f''. Since "''For every standard, finite set F, there is a finite set g such that {{tmath|f \in G}} for all f in {{itco|F}}''" (e.g. {{math|''g'' {{=}} ''F''}}), we may use Idealisation to derive "''There is a finite set G such that {{tmath|f \in G}} for all standard {{itco|f}}''."<!--  In other words, all standard sets can be contained in a finite set as elements. --> For any set ''S'', the intersection of ''S'' with the set ''G'' is a finite subset of ''S'' that contains every standard element of ''S''. ''G'' is necessarily nonstandard, by the ZFC [[Axiom of regularity|regularity]] axiom.