## TYPES OF SETS CLASS 11

For the purposes of mathematics a set is generally described as” a **well-defined collection of distinct objects**” by a well-defined collection is **meant a collection** which is such that, given any** object,** we may be able to decide whether the** object belongs** to the collection **or not**. By d**istinct mean**, objects on which are identical (same). The objects in a set are formed its numbers or elements. **Capital letters** A, B, C, D, E………., Y, Z etc. are used as number of set there are types of sets. We will discuss one by one with example

### SET OF NATURAL NUMBER:

Set of natural number denoted by **capital N.** this set has complete number not **fractional number**. Natural number has **complete** number not fractional number and start from 1 to undefined.

**EXAMPLE:**

N= {1,2,3,4,5,6,7,8…………….}

#### SET OF WHOLE NUMBER:

Set of whole number denoted by **capital letter.** W this set also has complete number, not fractional number.** Whole number** set has **complete number not fractional number and** start from 0 to undefined.

**EXAMPLE:**

W= {0,1,2,3,4,5,6…………………………}

##### SET OF INTEGERS:

Set of integers numbers denoted by **capital letter **Z this set also has complete number not fractional number. Whole number set has complete number** not fractional number** and **start from 0** to positive direction and 0 to negative direction to undefined.

Z = {………….-5,-4,-3,-2,-1,0,+1,+2,+3,+4,+5…………..}

##### SET OF ODD NUMBERS:

This set has **odd numbers positive** and **negative** direction and denoted by the symbol **capital letter O**, odd number is** complete** numeric number not a fractional number** ±1,±2,±3,……**

**EXAMPLE:**

O = {…………..-5,-3,-1,+1,+3,+5…………..}

##### SET OF EVEN NUMBERS:

This set has even numbers **positive and negative** direction and denoted by the **symbol capital letter E,** even number is complete numeric number not a fractional number ±2,±4,±6,……

**EXAMPLE:**

**E = {…………..-6,-4,-2,0+2,+4,+6…………..}**

##### SET OF RATIONAL NUMBER:

All numbers which can be written as** p/q** form is called rational number where p and q are a part of set of integer number **Z and q** **does not equal to zero.** A set of rational number can be expressed in the form. Set of rational number denoted by** capital letter Q**

**EXAMPLE:**

**Q = { x| x=p/q where p, q ∈ Z and q ≠ 0}**

##### SET OF IRRATIONAL NUMBER:

All numbers which cannot be written as **p/q** form is called irrational number **where p and q are a part of set** of integer number** Z and q does not equal to zero.** Set of irrational number **denoted by capital letter Q’** set of irrational number can be expressed in the form.

**EXAMPLE:**

**Q’ = { x| x ≠ p/q where p, q ∈ Z and q ≠ 0}**

##### SET OF REAL NUMBER:

union of set of **rational and irrational numbers** is called real number set of real number is denoted by R

**EXAMPLE:**

**R = Q ∪ Q’** (rational number ∪ irrational number)

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