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 distinct 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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