Singleton (set theory)/Definition

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This page requires references, it is on a to-do list for being expanded with them.
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Definition

Let [ilmath]X[/ilmath] be a set. We call [ilmath]X[/ilmath] a singleton if:

  • [ilmath]\exists t[t\in X\rightarrow\forall s(s\in X\rightarrow s\eq t)][/ilmath]
    • In words: [ilmath]X[/ilmath] is a singleton if: there exists a thing such that ( if the thing is in X then forall stuff ( if that stuff is in [ilmath]X[/ilmath] then the stuff is the thing ) )

References