# Set Theory

## Set Theory

A branch of mathematics introduced in the late 19th century by the German mathematician Georg Cantor.

The primitive notions of set theory are “set” and “membership”,from which common mathematical objects such as numbers, relations, functions, geometric properties, etc., can be reconstructed.

Sets are defined as collections of objects called elements, and we write $$x\in A$$ to indicate that x is an element of A. Two sets are equal if and only if they contain the same elements. In other words, we know everything about a set if we know what its elements are.

Therefore, we accept the extensional definitions $$\left { a,b,c \right }=\left { c,a,b \right }=\left { a,b,a,b,c,a,b,a \right }$$ of a set that contains the three elements a, b et c.