Set. Element of a Set
Множество. Элемент множества
What is a Set?
Definition: A set is a collection of distinct objects. The objects in a set are called elements.
Sets are denoted by capital letters: A, B, C, D, ...
Elements are listed inside curly braces { }:
A = {1, 2, 3, 4, 5}
This set A contains five elements: 1, 2, 3, 4, and 5
Examples of Sets:
- Set of vowels: {a, e, i, o, u}
- Set of even digits: {0, 2, 4, 6, 8}
- Set of primary colors: {red, blue, yellow}
Key Points:
- Elements must be distinct
- Order does NOT matter
- {1, 2, 3} = {3, 1, 2}
Visual Representation of a Set (Euler Diagram)
The diagram below shows the set A = {1, 2, 3, 4, 5}. The elements are placed inside a closed curve — this is the classic way of representing sets, called an Euler diagram.
Interactive visualization — available in the full lesson
Note: All five elements are located inside the closed curve. This means each of them belongs to set A. Any object outside the curve does not belong to set A.