Prerequisites for Analysis

This is the material which is covered in my Spoken Reals exercise.

I. Notions from Set Theory - ( ita - chapter 1 )
Introduction :
Description of Sets :
Union of Sets :
Intersection of Sets :
The Null Set :
Material Implication - if A then B :
Subsets :
Ordered Pairs :
The Cartesian Product of Two Sets :
Function from X to Y :

II. The Real Number System - ( ita - chapter 2 )
Introduction :
The Real Number System :
The Field Properties :
The Order Property :
The Least Upper Bound Property :
Main Consequences of the Field Properties :
A Field of Two Elements :
Main Consequences of the Order Property :
The Field Becomes Infinite :
Integral Exponents :
Absolute Values :
Main Consequences of the Least Upper Bound Property :
Existence of Square Roots :