Homotopy Type Theory
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Definition
Let be an Archimedean ordered integral domain with the integers being a integral subdomain of , with monic function . The tight apartness relation in is defined as
In set theory
Let be an Archimedean ordered integral domain with the integers being a integral subdomain of , with injection . An element is irrational if
Let us define the dependent type on
The type of irrational numbers in is defined as
is irrational if the type has a term.
The type of irrational numbers in is defined as:
In homotopy type theory
Let be an Archimedean ordered integral domain with the integers being a integral subdomain of , with monic function . The tight apartness relation in is defined as
Let us define the dependent type on
is irrational if the type has a term.
The type of irrational numbers in is defined as:
See also
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