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Introduction to Set Theory

Set theory is the branch of mathematics that is concerned with the study of sets, which are generally collections of objects. Although any type of object may be collected into a set and set theory is applied mostly to objects which are relevant to mathematics. The language of set theory may be used in the definitions of around all mathematical objects.

Defining Sets:

A set is defined as a collection of well-defined objects and each individual object is known an element of that set.

For example- the Months of a year from a set as

D = {January, February, March, April, May, June, July, August, September, October, November, December}

February is an element of the set D. We write it as February D

Main Topics in Set Theory: Defining Sets, Algebra of Sets, Descriptive Set Theory, Axiomatic Set Theory, Naive Set Theory, Hall's Theorem, Zermelo Set Theory, Lattice Theory, Model Theory, Logical Operations, Ordinal Numbers, Cardinal Numbers, Cantor's Paradox, Cantor's Theorem, Continuum Hypothesis, Infinite Set, Equivalence Classes, Partial Orders, Sperner's Theorem, Antisymmetric Relation, Binary Relation, Equivalenche Relation, Concurrent Relation, Symmetric Relation, Translation Relation, Bayes' Theorem, Set Operations, Boolean Representation Theorem, Kneser's Conjecture, Consistency Theorem