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Set Theory Questions and Answers | Examsegg Mathematics

Real Numbers

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Rational and irrational numbers taken together form the set of real numbers. This set is denoted by ‘R’.

Natural numbers = N = { 1,2,3,4,5,…}

Whole numbers = W = { 0,1,2,3,4,… }

Integers = Z = {…,-3,-2,-1,0,1,2,3,… }

Rational numbers = Q = { 2 / 3 , -5 / 7, -10 / -3,…} .
The elements of this set is in p/q form.q ≠ 0.

Irrational numbers = π ( π = 3.1415926535897932384626433832795 (and more...), √2, √3 ,many cube roots, golden ratio Φ, e Euler’s number etc.

Since all rational and irrational numbers can be represented on the number line, we call the number line as real no. line.
Real no. = R = { Natural numbers, whole numbers, Integers, Rational numbers, Irrational numbers}

N ⊂ W ⊂ Z ⊂ Q ⊂ IR ⊂ R

A real no. is either rational or irrational.
There is a real nos. corresponding to every point on the number line. Also, corresponding to every real no. there is a point on the number line.

Examples :

1) Every irrational number is a real no. State (T/F). Justify your reason.

Solution :
The above statement is True because real no. is a set of rational as well as irrational numbers.
2) Are the square roots of all positive integers irrational? If not, prove with an example.

Solution :
No, the square roots of all positive integers are not irrational.
For example, √4 = 2
√9 = 3
Here, 2 and 3 are rational number.
Fill in the blanks
1) Every point on the number line corresponds to -------- number.(Ans)
2) Every real no. is either ------- number or ------ number.(Ans)

Real No.

Real Numbers
Representation of real nos. on number line
Operations on Real nos.
Rationalization of denominator
Euclid Geometry

From real no. to number system

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