Homotopy Type Theory real numbers > history (Rev #7)

Definition

The type of real numbers \mathbb{R} is a locally (-1)-connected? Hausdorff sober? Archimedean ordered field with a compact? real unit interval? [0,1][0, 1].

Other types called ‘real numbers’

There are many other different types which are called real numbers in the literature, many of which are do not satisfy the same properties as listed above for the real numbers. These include:

  • Cauchy real numbers (disambiguation)

  • Dedekind real numbers (disambiguation page)

  • Eudoxus real numbers

  • localic real numbers? (opens are binary relations, type is a frame and lies in a higher universe in the hierarchy) and sigma-localic real numbers? (opens are functions into Sierpinski space, type is a $\sigma$-frame and lies in the same universe)

  • MacNeille real numbers? or Dedekind-MacNeille real numbers

  • real unit interval? based real numbers

    • Euclidean real numbers? or Escardo-Simpson real numbers

    • The various types of real numbers defined by Peter Freyd using various definitions of the co-algebraic real unit interval.

References

Revision on March 12, 2022 at 06:52:11 by Anonymous?. See the history of this page for a list of all contributions to it.