Order Axioms

• Trichotomy: exactly one of these holds: , ,
• Transitivity:
• Operation with addition:
• Operation with mutliplication:

Definitions

Triangular inequalities

Required proofs

• Triangular inequalities

Theorems

Caution

is not valid.

Let be a non-empty subset of which is bounded above and has an upper bound .

Let be a non-empty subset of which is bounded below and has an lower bound .