Homotopy Type Theory Cauchy real numbers (disambiguation) > history (Rev #4, changes)

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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?HoTT book real numbers , which is defined as the free homotopy complete initial metric space generated by a dense integral subdomain of the rational numbers, and called the Cauchy real numbers in the$R_{+}$-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

  real numbers for other types of real numbers

  for other types of real numbers

• premetric space

References