. (i) Why is Axiom 5, in the list of Euclid's axioms,considered a 'universal truth' ? (Note that the question is not about the 5" postulate.)
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Step-by-step explanation:
This axiom is known as a universal truth because it holds true in any field, and not just in the field of mathematics.
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Step-by-step explanation:
Axiom 5 states that the whole is greater than the part.
This axiom is known as universal truth because it holds in any field , and not just in the field of mathematics.
Let state 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 is considered the continent Asia.
- Then , latest considered a country India which belongs to India.
- 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 this a universal truth.
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