Implementation of mathematics in set theory: Difference between revisions

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Empty set, singleton, unordered pairs and tuples: Swapped headings and definitions, made math layout consistently LaTeX, fixed spacing
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== Empty set, singleton, unordered pairs and tuples ==
These constructions appear first because they are the simplest constructions in set theory, not because they are the first constructions that come to mind in mathematics (though the notion of finite set is certainly fundamental!)
The empty set is the unique set with no members:
 
:<math>\emptyset \, \overset{\mathrm{def.}}{=} \{x \mid x \neq x\}</math>
In NFU, there are also urelements with no members.