TopIn mathematics, numbers are defined in certain types like rational number and irrational number, but the question arises the Set of all Rational and Irrational Numbers is called what?
The perfect answer of this question is the set of all rational and irrational numbers is called as a Real Numbers. Now for justifying this answer, we discuss history of number system -
All kind of numbers in mathematics are part of real numbers and the real numbers are divided into rational number, which is written in numerator and denominator form, means in (a / b) here ‘a’ and ‘b’ are integers and the other part of real numbers are irrational number, those numbers which are not part of Rational Numbers are called as an irrational numbers like √2, ‘e’ (exponential), pie (π) etc. Now we take some examples which define the set of all rational and irrational numbers is called as a real numbers-
Example 1: Find the rational and irrational numbers from the following real number set-
R = 2 / 5, -√10, 0, 2.9, -5, 4, -1 / 3, √6, -71/5?
Solution: Given real number set is a Combination of all kind of numbers where rational and irrational numbers exist. So, now we describe rational and irrational number from the given real number set -
Rational number = 2 / 5, 0, 2.9, -5, 4, -1/ 3,
Natural number = 4
Whole number = 0, 4
Integer number = 0, -5, 4
After evaluation of rational number, now we calculate irrational number set from the given real number set -
Irrational number = -√10, √6, -71/5,
With the help of this example, now we can say that the set of all rational and irrational numbers is called as a real number set.