Why is Axiom 5, in the list of Euclid's axioms, considered a ' universal truth'? (note the the question is not about the fifth postulate).
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Answer:
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.
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Answer:
Axiom 5 of Euclid's Axioms states that - “The whole is greater than the part.”
This axiom is known as a universal truth because it holds true in any field of mathematics and in other disciplinarians of science as well.
Let us consider a line segment AB. Mark two points P and Q on
AB is a whole part.
It is divided into three parts: AP, PQ, QB.
AB = AP + PQ + QB
Thus, we see that
AB > AP
AB > PQ
AB > QB
Hence, AB (whole) is greater than its parts i.e, AP, PQ, and QB.
Let's take some practical facts to understand this.
•India is a part of the world which concludes the world is larger than India. Here the world is a whole whereas, India is just a part of it.
Therefore, it is true that the whole is greater than the part that is considered as universal truth.