سوال ۲۱ کنکور ارشد ریاضی ۱۴۰۵

Read the following passage (Passage 3) and answer the question.

PASSAGE 3:

By principles of mathematics, we mean a body of propositions which arise in mathematical demonstrations and which serve as premises for deduction. These principles are not proven. In so-called classical mathematics, or more precisely, the classical method of explicating mathematics, which was in current use up until the end of the nineteenth century, three types of mathematical principles were distinguished: the definitions, the axioms and the postulates. [1]

(Paragraph 2) A definition was understood to be a proposition indicating what a given thing is. Thus, for instance, Euclid defined parallels as two straight lines which are located on the same plane, and which when extended to infinity in both directions do not meet in either direction. We will simply point out here that a definition in no way proves the existence of the defined object. [2] Thus, in proposition XXI of Book I of the Elements, Euclid proves that parallels exist by demonstrating that one may draw through a point situated outside a straight line another straight line that does not cut the first.

(Paragraph 3) An axiom was understood to be a proposition “evident in itself.” For example: the whole is greater than any of its parts. An axiom, understood in this way, is not provable. [3] The unverifiability of the axiom derives from its very definition. One cannot prove what is evident in itself and constitutes in a way a truth of reason. But it must be pointed out in this regard that the concept of “evidence” is extremely relative. Thus the proposition, which we have just made, was considered as being evident, up until the time when Galileo demonstrated that there were certain objects later called infinite sets—of which a part was as great as the whole. [4]

Which of the following techniques is used in paragraph 2?