## Quick Reference

A set *S* on which the relation < is defined, satisfying the following properties:*x,y,z* in *S*, if *x* < *y* and *y* < *z*, then *x* < *z**x,y* in *S*, then exactly one of the following three possibilities is true: *x* < *y*, *x* = *y*, or *y* < *x**T* is any nonempty subset of *S*, then there exists an element *x* in *T* such that *x* = *y* or *x* < *y*, i.e. *x* ≤ *y* for all *y* in *T* This relation < is said to be a **well ordering** of the set *S*.

*x,y,z* in *S*, if *x* < *y* and *y* < *z*, then *x* < *z*

*x,y* in *S*, then exactly one of the following three possibilities is true: *x* < *y*, *x* = *y*, or *y* < *x*

*x* < *y*, *x* = *y*, or *y* < *x*

*T* is any nonempty subset of *S*, then there exists an element *x* in *T* such that *x* = *y* or *x* < *y*, i.e. *x* ≤ *y* for all *y* in *T*

*x* = *y* or *x* < *y*,

*Subjects:*
Computing.