Order Theory (subject)
Contents
Overview
Order theory is the study of certain kinds of relations on sets. Abstract algebra covers the case of a set equipped with functions (which are rightunique relations that map everything in their domain to something), order theory deals instead with relations that are at the very least, transitive and then branches off into lattices  which is studying the directed graphs (or digraphs) that result from various kinds of orderings, called lattice theory.
Required for
Some order theory is desired for parts of analysis, for this I recommend the reader know at least about partial orderings and posets, this is because topics like limits require some notion of ordering, however since year 2 children are taught to "pretend [ilmath]<[/ilmath] is a crocodile, it wants to eat the bigger number" and is fully aware that [ilmath]5<2[/ilmath] and such. However it cannot hurt.
Statistics
The order theory project contains:
 Definitions  16 pages
 Theorems, lemmas and corollaries  3 pages
 (all pages)  23 pages
