# MAT299 Chapter Notes - Chapter 4: Partially Ordered Set, Total Order, Natural Number

## Document Summary

In this extension section, more details of binary relation of a set are discussed as follows: recall that the cartesian product of domain set and co-domain set represents all possible binary relation between these two sets. If element a is equal to another element b, then b also equals to a (symmetric) If an element a is less than or equal to element b, it is not necessary that b is less than or equal to a (asymmetric) If element a is less than element b, b must not be less than a (not symmetric) If element a is less than element b, and b is less than element c, then a is less than c (transitive: every element must be less than or not less than one another (trichotomy) If we enumerate r=b- q a by changing the value of q; say, let b=20 and. A=3, then the resulting set of remainder should be as follows: