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)
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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)
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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.
* 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.
* 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.