Question

Why is Axiom 5, in the list of Euclid's axioms, considered a 'universal truth'? ( Note that the question is not about the fifth postulate)

Answer 1

Axiom 5 states that the whole is greater than the part.

This axiom is known as a universal truth because it holds true in any field, and not just in the field of mathematics.

Let us take two cases - one in the field of mathematics, and one other than that.

• Case 1

* Let 't' represent a whole quantity and only a, b, c are parts of it.

* t = a + b + c

* Clearly, t will be greater than all its parts a, b and c.

* Therefore, it is rightly said that the whole is greater than the part.

• Case 2

* Let us consider the continent Asia.

* Then, let us consider a country India which belongs to Asia.

* India is a part of Aisa and it can also be observed that Asia is greater than India.

* That is why we can say that the whole is greater than the part.

* This is true for anything in any part of the world and is thus a universal truth.

Answer 2

$\huge{\underline{Solution}}$

↪ Axiom 5 states that the whole is greater than the part.

↪ This axiom is known as a universal truth because it holds true in any field, and not just in the field of mathematics.

↪ Let us take two cases − one in the field of mathematics and one other than that.

★ Case I

↪ Let t represent a whole quantity and only a,b,c are parts of it.

$\sf{t=a+b+c}$

↪ Clearly, t will be greater than all its parts a,b and c.

↪ Therefore, it is rightly said that the whole is greater than the part.

★ Case II

⇝ Let us consider the continent Asia.

⇝ Then, let us consider a country India which belongs to Asia.

⇝ India is a part of Asia and it can also be observed that Asia is greater than India.

⇝ That is why we can say that the whole is greater than the part.

⇝ This is true for anything in any part of the world and is thus a universal truth.