Question

discuss elementary properties of set theory.​

Answer 1

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★In mathematics, a set is a collection of distinct things considered as a whole. The objects of a set are called elements or members. The elements of a set can be anything: numbers, our class, English alphabets, or even another set.

★Two sets are equal if they contain exactly the same elements. That is, set A is equal to set B if every element of A is also an element of B, and every element of B is also an element of A. The order in which the elements of a set are listed in its definition is irrelevant.

Answer 2

Answer:

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❥Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics.

❥The language of set theory can be used to define nearly all mathematical objects.Set theory is commonly employed as a foundational system for mathematics, particularly in the form of Zermelo–Fraenkel set theory with the axiom of choice.

❥Beyond its foundational role, set theory is a branch of mathematics in its own right, with an active research community. Contemporary research into set theory includes a diverse collection of topics, ranging from the structure of the real number line to the study of the consistency of large cardinals.