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.

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

Since objects are counted in natural numbers and are therefore regarded as natural numbers, we have no concerns about 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.

Before we discuss irrational numbers, let's look at a few instances of them.

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.

Therefore, a great deal of information can be better understood by using irrational numbers. These numbers do exist in nature, even though the average person may not find them particularly easy to understand. The point is, these numbers simplify the understanding of a great deal of information.

In actuality, even complex numbers—which even mathematicians found extremely challenging to understand until the 17th century—make electromagnetic phenomena and the flow of current through electronic circuits using resistances, inductance, and capacitors easier to understand.

Therefore, even though the average person may find many concepts in mathematics to be confusing or difficult to understand, they do exist in some form and are necessary to comprehend nature.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

Irrational numbers exist because there are quantities that cannot be expressed as the ratio of two integers. These numbers have non-repeating and non-terminating decimal expansions. They arise from mathematical concepts such as square roots of non-perfect squares or the ratio of a circle's circumference to its diameter.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7