Notes on Cambridge Maths

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Linear order

A linear order (or total order) on a set is a relation on that is:

  1. irreflexive
  2. transitive
  3. trichotomous
    We say is linearly ordered by ,
    or simply is a linearly ordered set.

Notation

For write
for
and for ” or ”
This satisfies:

  1. reflexivity
  2. antisymmetric:
  3. transitive:
  4. trichotomous:

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