search

wangbinyq / personal-wiki

2 stars 0 forks source link

abstract algebra #20

Closed wangbinyq closed 7 years ago

wangbinyq commented 7 years ago

free text book: http://abstract.ups.edu/download/aata-20170805.pdf

1 Preliminaries

1.1 proofs

Definition:

  1. axioms: Some rules about a collection of objects S's structure.
  2. statement: An assertion that is either true or false.
  3. proof: A convincing argument about the acuracy of a statement.
  4. proposition: an statement can be proved to be true.
  5. theorem: a proposition of major importance.
  6. lemmas:
  7. corollaries:

1.2 Set and Equivalence Relations

Defintion:

  1. set: is a well-defined collection of objects; that is, it is defined in such a manner that we can determine for any given object $x$ whether or not $x$ belongs to the set.
  2. objects or members: belong to a set.