Question

Give an example of the following axiom from your experience.
the whole is greater than the part.

Answer 1

Hint: To find an example of the given axiom, we need to first understand what an axiom is and the uses of the axiom. We will also note down some famous axioms so that we get a better hold on the term. Once we are well versed with the term “axiom”, we will look around us and also recall the mathematical properties and results to find an example for the given axiom. This example can be anything from the tangible world around us, the things we see in our daily life or from the intangible mathematical results.

Complete step by step answer:
We are given the axiom “the whole is greater than the part” and we are asked to find the examples of this axiom. Before this, we will see how a statement can qualify as an axiom. According to the Cambridge English dictionary, “an axiom is a statement or principle that is generally accepted to be true, but need not be so” or “a formal statement or principle in mathematics, science, etc., from which other statements can be obtained”. Therefore, axiom is a statement which is considered to be true.
Thus, we can say that “the whole is greater than the part” is true and we can also verify with our experience it from the outside world. Consider that we have a pizza, with 8 slices, then each of the slices will be smaller than the whole pizza and the pizza is greater than the smaller pieces.
Suppose A, B and C are three terms, such that A + B = C.
This means, C is whole and A and B are parts of C. We can safely say that C > A and C > B.

Note: The given axiom “the whole is greater than the part” is a very famous axiom known as the Euclid’s Axiom, given by the great Greek mathematician Euclid. It is one of the fundamental axioms of mathematics and many theorems are based on this axiom.