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Disambiguation page
There are many different types which are called Cauchy real numbers in the literature. These include:
sequential Cauchy real numbers? , which is 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 sequential Cauchy real numbers? and modulated generalized Cauchy real numbers?, where the modulus of convergence is structure rather than mere property
HoTT real numbers? , which is defined as the free complete metric space generated by a dense integral subdomain of the rational numbers, and called the Cauchy real numbers in theHoTT book.