#
The Order Property
*
ita
*

##
O1:
Trichotomy
( *a*>*b*, *a*=*b*, *or a*<*b* )

O2:
Transitivity
( *a*>*b and b*>*c implies a*>*c* )

O3:
(the sum of the greater) > (the sum of the less)

O4:
(the product of the *positive* greater) > (the product of the *positive* less)

O5:
Rules of Sign in Addition and Multiplication

O6:
*a·a* is greater than or equal to zero.

O7:
Positive numbers have positive reciprocals.

O8:
Larger positive numbers have smaller reciprocals.

O9:
Elementary Arithmetic, Natural Numbers, Integers, Rational Numbers

Converted [ in part ] by *Mathematica*
December 4, 2007;

Edited 12 May 2010