Home
Class 9
MATHS
Why is Axiom 5, in the list of Euclid’s...

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.)

Text Solution

Verified by Experts

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. 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. ...
Promotional Banner

Similar Questions

Explore conceptually related problems

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.

Given the sets A = {1, 3, 5} , B = {2,4, 6} and C = {0, 2,4, 6, 8} , which of the following may be considered as universal set (s) for all the three sets A, B and C (i) {0, 1, 2, 3, 4, 5, 6} (ii) phi (iii) {0,1,2,3,4,5,6,7,8,9,10} (iv) {1,2,3,4,5,6,7,8}

(a) A certain mass of gas initially at (1L, 5 atm, 300 K) is expanded reversible and isothermally to final volume of 5L , calculate the work done by the gas and heat supplied in this process to the gas. (b) Now, if the gas is released to initial position by compressing it using an external constant pressure of 5 atm. Find work done on the gas in this process and heat rejected by gas (c ) In the above two processes, what is the net gained by surroundings ? [Note: From above question see that surrounding has done extra work on the system but system has returned that work in the form of heat to surrounding and work is considered on organized form of energy while heat as an unorganised form hence in the above process, there must be net increment in randomness of universe which be called Entropy, soon]