       # ALGEBRA OF SETS

INTRODUCTION TO SET THEORY

Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics.

IDENTITY AND CARDINALITY OF SETS

Equality of sets or Identity of sets: A set is said to be equal to set if both sets have the same elements or members of the sets, i.e. if each element of set also belongs to each element of set , and each element of set also belongs to each element of set . Mathematically it can be written as A ⊂ B and B ⊂ A
In mathematics, the cardinality of a set is a measure of the "number of elements of the set". For example, the set A = {2, 4, 16,24} contains 4 elements, and therefore A has a cardinality of 4.

SET OPERATIONS/SET THEORETICAL NOTATIONS
The union of two sets P and Q is a set containing all elements that are in P or in Q (possibly both). It is denoted by P∪Q.
The intersection of two sets P and Q, denoted by P∩Q, consists of all elements that are both in P and Q.
The difference (subtraction) is defined as follows. The set P−Q consists of elements that are in P but not in Q.

SET OF NUMBERS

It is defined as any number that is, a solution to a polynomial equation with rational coefficients. All Rational and Irrational numbers. They can also be positive, negative or zero.
Mathematically, set of numbers can include:
1) Natural numbers, 2) Integers, 3) Rational numbers, 4) Irrational numbers,
5) Real numbers