Why do we need rational and irrational numbers?

1 Answer
Daniel L.
Apr 3, 2016

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)

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