Set definition and forms to write sets and set of numbers.

SET:
         A well defined collection of {distinct} objects is called a set.
Examples :
The objects are called the elements or members of the set.
Sets are denoted by capital letters A, B, C …, X, Y, Z.
The elements of a set are represented by lower case letters

a, b, c, … , x, y, z.

TABULAR FORM

Listing all the elements of a set, separated by commas and enclosed within braces

or curly brackets {}.

EXAMPLES

In the following examples we write the sets in Tabular Form.

A = {1, 2, 3, 4, 5}is the set of first five Natural Numbers.

B = {2, 4, 6, 8, …, 50} is the set of Even numbers up to 50.

DESCRIPTIVE FORM:

Stating in words the elements of a set.

EXAMPLES

Now we will write the same examples which we write in Tabular

Form ,in the Descriptive Form.

A = set of first five Natural Numbers.( is the Descriptive Form )

B = set of positive even integers less or equal to fifty.

( is the Descriptive Form )

SET BUILDER FORM:

Writing in symbolic form the common characteristics shared by all the

elements of the set.

EXAMPLES:

Now we will write the same examples which we write in Tabular as well as Descriptive

Form ,in Set Builder Form .

A = {x ÎN / x<=5} ( is the Set Builder Form)

B = {x ÎE / 0 < x <=50} ( is the Set Builder Form)

SETS OF NUMBERS:

1. Set of Natural Numbers

N = {1, 2, 3, … }

2. Set of Whole Numbers

W = {0, 1, 2, 3, … }

3. Set of Integers

Z = {…, -3, -2, -1, 0, +1, +2, +3, …}

= {0, ±1, ±2, ±3, …}

{“Z” stands for the first letter of the German word for integer: Zahlen.}

4. Set of Even Integers

E = {0, ± 2, ± 4, ± 6, …}

5. Set of Odd Integers

O = {± 1, ± 3, ± 5, …}

6. Set of Prime Numbers

P = {2, 3, 5, 7, 11, 13, 17, 19, …}

7. Set of Rational Numbers (or Quotient of Integers)

Q = {x | x = ; p, q ∈Z, q ≠ 0}

8. Set of Irrational Numbers

Q = Q′ = { x | x is not rational}

For example, √2, √3, π, e, etc.

9. Set of Real Numbers

R = Q ∪ Q′

10. Set of Complex Numbers

C = {z | z = x + iy; x, y ∈ R}

thanks 

Prepared By Syed Umer Farooq

BLOG: http://bestnotes4students.blogspot.com/