A Venn diagram illustrating the intersection of two sets
3rd century BC Greek mathematician Euclid (holding calipers), as imagined by Raphael in this detail from The School of Athens (1509–1511)

Mathematical notation for describing a set by enumerating its elements, or stating the properties that its members must satisfy.

- Set-builder notation

Set theory has set-builder notation. It can create any set that can be defined. This allows it to create Uncountable sets. Type theories are syntactic, which limits them to a countably infinite terms. Additionally, most type theories require computation to always halt and limit themselves to recursively generable terms. As a result, most type theories do not use the Real numbers but the Computable numbers.

- Type theory
A Venn diagram illustrating the intersection of two sets

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