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Disambiguation page
There are many different types which are called real numbers in the literature. These include:
Euclidean real numbers? or Escardo-Simpson real numbers
MacNeille real numbers? or Dedekind-MacNeille real numbers
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 unit interval.