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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Josie 2 months 2021-11-28T10:44:25+00:00 2 Answers 0 views 0

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    2021-11-28T10:45:45+00:00

    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.

    0
    2021-11-28T10:46:04+00:00

    \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.

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