why do we need a set of rational numbers ?
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Answer:
Explanation:
All subsets of real numbers were created to extend the mathematical operations we can perform on them.
First set was natural numbers (
N
) .
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 (
Z
)
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 (
Q
)
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
√
2
which is an example of irrational number.
If we add rational and irrational numbers we get the whole set of real numbers (
R
)