Question

Why do irrational numbers exist?

Answer 1

Though common person may find many things in mathematics as incomprehensible or difficult to understand, they do exist in some form and serve the purpose of understanding of nature.

Explanation:

It appears that by the question "why do irrational numbers exist?#, questioner means, whether irrational numbers exist in nature.

We have no qualms about natural numbers, as objects are counted in natural numbers and as such they are considered as natural numbers.

What about fractions? We do understand what is meant by `1/2` of a loaf of bread, `3/8` of a pizza and so on. So there are perhaps no issues regarding fractions.

Coming now to irrational numbers, let us first see some examples of irrational numbers.

One example is `sqrt2` and we understand `sqrt2` as it is the length of a diagonal of a unit square. Similarly `sqrt3` is height of an equilateral triangle, whose one side is `2`. Irrational number `pi` is the ratio of circumference of a circle to its diameter or circumference of a circle of unit diameter.

Hence many things can be comprehended better by irrational numbers. So, they do exist in some form in nature, though the a common person may not find it easy to comprehend. The fact is these numbers make understanding of many thing easy.

In fact, even complex numbers, though were very difficult to comprehend even by mathematicians till 17th century, make easy to understand electromagnetic phenomena and flow of current through electronic circuits using resistances, inductance and capacitors.

Hence, though common person may find many things in mathematics as incomprehensible or difficult to understand, they do exist in some form and serve the purpose of understanding of nature.