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 rational numbers. * [[generalized Cauchy real numbers]], which is defined using all Cauchy nets of 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 the rational numbers, and called the Cauchy real numbers in the [[HoTT book]]. ## References ## [[HoTT book]] * Auke B. Booij, The HoTT reals coincide with the Escardó-Simpson reals, ([https://arxiv.org/abs/1706.05956](abs:1706.05956)) * Auke B. Booij, Extensional constructive real analysis via locators, ([https://arxiv.org/abs/1805.06781](abs:1805.06781))