The Order Property ita

Preliminary

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

Exponentiation

Absolute Values


Converted [ in part ] by Mathematica      December 4, 2007;
Edited 12 May 2010