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Ideas and Symbols to be Used with the Order Property

*"*The [real numbers *a* in **R+ **(previously referred to as 'R plus')] will of course be called *positive*, those such that -*a* [is in **R+** will be called] *negative*. From the [order property] we shall deduce all the usual rules for working with inequalities.*"* *(see ita-1-2-2-pg19)*

*"*To be able to express the consequences of [the order property] most conveniently we introduce the relations > and < . For *a*, *b* [in **R**] either of the expressions *a*>*b* or *b*<*a* (read respectively as '*a * is greater than *b*' and '*b* is less than *a*') will mean that *a*-*b* [is in **R+**]. Either of the expressions or will mean that *a*>*b* or *a*=*b*.*"* *(see ita-2-2-3-pg19)*

Note that the greater and less than symbols point toward the smaller number. We may use this as a reminder by thinking that the width of the symbol indicates the size of the number: The wide end is at the larger number. Also: Expressions which have real numbers separated by the greater than, less than, or equality symbols can be referred to as *relations*.

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