seplrcnite

valsi

seplrcnite

type

fu'ivla

creator

krtisfranks

time entered

Tue Feb 9 21:24:36 2016  

English

Definition #68381 - Preferred

 

definition

x₁ is a Dedekind cut associated with number/point x₂ of totally ordered set x₃

notes

Let MATH

$x_3 = (X, <)$

x₃ = (X, < ) be an ordered set formed by (underlying) set X endowed with order relation '<'. x₂ is a member of X; lethe the singleton of x₂ (the set containing only and exactly x₂) be denoted by Y. Then x₁ constitutes an ordered pair of sets (A, B) such that A and B are mutually disjoint subsets of X, A is closed downwardly/lesserwardly under '<', B is closed upwardly/greaterwardly under '<', x₂ is not an element of A, and the union of A with B and Y equals exactly X.

gloss words

• Dedekind cut

created by

krtisfranks

vote information

1

time

Tue Feb 9 21:24:36 2016

Examples

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