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Disambiguation page
There are many different types which are called Cauchy real numbers in the literature. These include:
Cauchy real numbers, which is sometimes defined using Cauchy sequences of a dense integral subdomain of the rational numbers.
generalized Cauchy real numbers, which is defined using all Cauchy nets of a dense integral subdomain of the rational numbers in a universe.
modulated Cauchy real numbers and modulated generalized Cauchy real numbers?, where the modulus of convergence is structure rather than mere property
HoTT book real numbers , which is defined as the homotopy initialCauchy structure-Cauchy structure for the positive terms of a dense integral subdomain of the rational numbers , and called the Cauchy real numbers in the HoTT book.