# What are the basic concepts of set theory?

## What are the basic concepts of set theory?

Sets are well-determined collections that are completely characterized by their elements. Thus, two sets are equal if and only if they have exactly the same elements. The basic relation in set theory is that of elementhood, or membership.

## What is the purpose of set theory?

Set theory is important mainly because it serves as a foundation for the rest of mathematics–it provides the axioms from which the rest of mathematics is built up.

**What does or mean in set theory?**

Table of set theory symbols

Symbol | Symbol Name | Meaning / definition |
---|---|---|

A⋃B | union | objects that belong to set A or set B |

A⊆B | subset | A is a subset of B. set A is included in set B. |

A⊂B | proper subset / strict subset | A is a subset of B, but A is not equal to B. |

A⊄B | not subset | set A is not a subset of set B |

### Where is set theory used?

Set theory is used throughout mathematics. It is used as a foundation for many subfields of mathematics. In the areas pertaining to statistics, it is particularly used in probability. Much of the concepts in probability are derived from the consequences of set theory.

### How many types of set theory are there?

Ans. 3 The different types of sets are empty set, finite set, singleton set, equivalent set, subset, power set, universal set, superset and infinite set.

**What is the importance of set?**

The purpose of sets is to house a collection of related objects. They are important everywhere in mathematics because every field of mathematics uses or refers to sets in some way. They are important for building more complex mathematical structure.

## Who introduced set theory?

Georg Cantor

Between the years 1874 and 1897, the German mathematician and logician Georg Cantor created a theory of abstract sets of entities and made it into a mathematical discipline. This theory grew out of his investigations of some concrete problems regarding certain types of infinite sets of real numbers.