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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!)
:<math>\emptyset \, \overset{\mathrm{def.}}{=} \{x \mid x \neq x\}</math>
For each object <math>x</math>, there is a set <math>\{x\}</math> with <math>x</math> as its only element:
:<math>\displaystyle\{x\} \overset{\mathrm{def.}}{=} \{y \mid y = x\}</math>
For objects <math>x</math> and <math>y</math>, there is a set <math>\{x,y\}</math> containing <math>x</math> and <math>y</math> as its only elements:
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