Question

Why do we need rational and irrational numbers?

Answer 1

See explanation.

Explanation:

All subsets of real numbers were created to extend the mathematical operations we can perform on them.

First set was natural numbers (`NN`) .

In this set only addition and multiplication could be done.

To make substraction possible people had to invent negative numbers and expand natural numbers to integer numbers (`ZZ`)

In this set multiplication, addition and substraction were possible but some division operatins could not be done.

To extend the range to all 4 basic operations (addition, substraction, multiplication and division) this set had to be extended to set of rational numbers (`QQ`)

But even in this set of numbers not all operations were possible.

If we try to calculate the hypothenuse of an isosceles right triangle, whose catheti have length of `1` we get a number `sqrt(2)` which is an example of irrational number.

If we add rational and irrational numbers we get the whole set of real numbers (`RR`)