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 [[net]]s 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 initial $R_{+}$-Cauchy structure for $R_{+}$ the positive terms of a dense integral subdomain $R$ of the [[rational numbers]] $\mathbb{Q}$, and called the Cauchy real numbers in the [[HoTT book]]. ## See also ## * [[real numbers]] for other types of real numbers ## References ## * Auke B. Booij, The HoTT reals coincide with the Escardó-Simpson reals, ([abs:1706.05956](https://arxiv.org/abs/1706.05956)) * Auke B. Booij, Extensional constructive real analysis via locators, ([abs:1805.06781](https://arxiv.org/abs/1805.06781)) * Auke B. Booij, Analysis in univalent type theory ([pdf](https://etheses.bham.ac.uk/id/eprint/10411/7/Booij2020PhD.pdf)) * Univalent Foundations Project, [[HoTT book|Homotopy Type Theory – Univalent Foundations of Mathematics]] (2013)