In modern mathematics set theory, elements are every object that constitutes a set. A collection consists of elements, and each object that makes up the collection is also called an element. For example, 1, 2,3 in the set {1, 2,3} are all elements of the set.

Concept:

Set is one of the basic concepts in mathematics. The totality of things with certain attributes is called "set", and elements are everything that constitutes a set.

The branch of mathematics that studies set operations and their properties is called set theory or set theory. The definition of set is very broad, not limited to mathematics, but also widely used in production and life. All things with specific attributes that make up a specific set can be called elements, so the definition of elements is also very broad.

Some specified objects are grouped together to form a set, where each object is called an element.

Russell's paradox

Divide all sets into two categories. The set in the first category takes itself as an element, while the set in the second category does not take itself as an element. Assuming that the set of the first kind is p and the set of the second kind is q, there are: P={A∣A∈A}, Q={A∣A? Answer.

Question: Q∈P or Q? p？

If Q∈P, then according to the definition of the first set, there must be Q∈Q, and any set of q has a? The nature of a, because Q∈Q, so q? Ask, lead to contradictions.

If q? P, according to the definition of the first set, A∈A, then Q? Q, and according to the definition of the second set, so Q∈Q, according to the definition of the first set, A∈A, so Q∈P, leads to contradictions.

This is the famous "Russell paradox". Russell's paradox has some popular explanations, such as Barber's paradox.

In order to eliminate this paradox, set theory stipulates that all sets cannot take themselves as elements.

There are only two possibilities between element a and a given set a:

1, A belongs to the set A, which is expressed as an element of the set A and recorded as A ∈ A ..

2.A does not belong to the set A, which means that A is not an element of the set A, and it is recorded as A? Answer.