Mathematics
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).
Answer
Axiom 5 states that :
'Whole is always greater than its part'. This is a 'universal truth' because it holds true in any field of mathematics and in other disciplinarians of science as well.
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.
Such that :
t = a + b + c
Clearly, t will be greater than all of its parts a, b and c. Therefore, it is rightly said that the whole is greater than the part.
Case 2 — Let us consider 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.
Related Questions
Consider two ‘postulates’ given below:
(i) Given any two distinct points A and B, there exists a third point C which is in between A and B.
(ii) There exist at least three points that are not on the same line.
Do these postulates contain any undefined terms? Are these postulates consistent? Do they follow from Euclid’s postulates? Explain.
In Question 4, point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point.
In figure, if AC = BD, then prove that AB = CD.
