Why do we need rational and irrational numbers?

1 Answer
Apr 3, 2016

See 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#)