Question

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

Answer 1

Hint: Part of something is always smaller than its whole. Here we have to prove that it is universal truth .For proving it universal truth, we have to show that it is applicable everywhere either mathematically or logically.

Complete step-by-step answer:
First of all let us see what axioms and postulates are:
Axioms: These are the assumptions made by Euclid, which were not to be proved and are used throughout mathematics not specifically linked to geometry.
Postulates: On the other hand, these are assumptions that were specific to geometry only.
The given question is about the axiom 5 of Euclid.
Let us now see the statement for Euclid’s axiom 5:
It states that ‘The whole is always greater than the part.’
It gives the definition of ‘greater than’.
This axiom is known as universal truth because it is valid always for everything in the universe.
We can prove this statement by taking any example.
Let us take a mathematical example.
$12 + 15 = 27$ .
Here the sum of 12 and 15 is 27. So, the whole that is formed by the addition of two numbers is greater than its individual number or we can say the parts i.e. 12 and 15 are smaller than the whole number that is formed by their addition.
Let us take another example.
Suppose you ordered a cake on your birthday and you cut a piece of cake with a knife. Then the piece that you cut from the whole cake is smaller than the whole cake or it is just a part of it.
Therefore, we can say that axiom 5 of Euclid is universal truth.

Note: You should remember the fifth axiom of Euclid. Do not get confused with the fifth axiom and fifth postulate. Here in this question it is clearly mentioned about the fifth axiom not fifth postulate. To show it is universally valid means it is applicable for everything in the universe.