Sets, domains and attributes.

Sets - a collection of properly identified objects that satisfy the conditions of ownership (domains).

This condition can be expressed both verbally and with the help of functional dependencies.
For example: integers from 0 to 100.
The set itself may be an element of other sets.
The database uses ordered sets .
In addition to ordered sets, there are extended sets .
The main formal object of extended sets is a complex .
The complex determines the basic relation of the i-th accessory.
For example: if X is the i-th element of the set Y, then X is in the i-th position of this set and is written in the set using the upper index (a1, b2, a3).
The set (a1, b2, a3) allows the use of duplicates, i.e. place identical values ​​in the set.
There are sets for which one and the same nature can be defined, such sets are called domains .
For example, the domain of integers can define a set of attributes: phone number, salary, student ID number, etc.
The main objective of this stage of conceptual design is the definition and coordination of all domains for database attributes.
Relationships, Entities, and Connections
Consider a series of sets, each of which defines a certain type of object.
For example: surname - {Ivanov, Petrov, Sidorov}
course - {2, 4, 3}
average ball {3.5, 4.5, 5}
Sets can be interpreted using domains, roles, and attributes.
{Ivanov, Petrov, Sidorov}
Personality - {2, 4, 3}
{3.5, 4.5, 5}
Aggregation of sets allows formulating more complex types.
A relation is an aggregate built on sets, that is, these are connections between sets that show the mutual influence of the elements of one set on another.
Attitudes can be given a different semantic meaning, that is, to relate each tuple of a relationship to a specific entity. In tables, a tuple is a record, and an entity is a table name.
Entity is a data element belonging to objective reality.
For example: employee, bargain, house.
As a rule, an entity is a noun, and an entity type can be defined as an aggregation of attributes.
An entity type may correspond to a generalization of one or more entity types.
For example:

Student:

Seller:

Between individual types of entities, in addition to generalization, you can use a different interpretation, namely communication .