Let be the rational numbers and let be the type of positive rational numbers. Given a directed type , a term is a limit of a net or that converges to if comes with a term
The type of all limits of a net is defined as
A limit of a sequence is usually written as
In premetric spaces
Let be a dense integral subdomain of the rational numbers and let be the positive terms of . Let be a -premetric space. Given a directed type , a term is a limit of a net or that converges to if comes with a term
The type of all limits of a net is defined as
Cauchy approximations
Let be a dense integral subdomain of the rational numbers and let be the positive terms of .