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Definitions to memorize. 1. Sets relations and functions.
 

Summary: Definitions to memorize.
1. Sets relations and functions.
A and A where A is a family of sets.
A family of sets is disjointed.
The definition of a relation. r s, r|A, r[A] where r, s are relations and A is a
set.
Cartesian product.
The definition of an equivalence relation on a set.
Partial, linear and well ordering.
Greatest lower bound and least upper bound.
The definition of an interval.
The definition of a function.
2. Initial segments, well ordering and the Axiom of Choice.
The definition of an initial segment.
3. The natural numbers and arithmetic.
The definitions of finite, infinite, countable and uncountable.
4. Introduction to the theory of infinite sets.
5. The real numbers.
The definition of absolute value. (Make sure you understand the context.)
Completely ordered field.

  

Source: Allard, William K. - Department of Mathematics, Duke University

 

Collections: Mathematics