subset

Thân thiện

A Venn diagram shows one circle as a subset of a larger circle.

Definition

Noun: A subset is a set in which every member (or element) is also a member of another, larger set. In simpler terms, it is a collection of items that is entirely contained within a bigger collection.

Usage

The word subset is used primarily in mathematical, logical, and technical contexts to describe a part of a whole group. It is often used with the prepositions "of" or "within."

Examples

• The set {2, 4} is a subset of the set {1, 2, 3, 4, 5}.
• This survey only targeted a specific subset of the population: young urban professionals.
• In biology, mammals are a subset of vertebrates.

Advanced Usage

• Proper Subset: A subset that is strictly contained within another set and is not equal to it. Often denoted by the symbol ⊂.
  • Example: The set of positive integers is a proper subset of the set of all integers.
• Subset Relation: The relationship where one set is a subset of another.
  • Example: The subset relation between sets is a fundamental concept in set theory.

Variants and Related Words

• Superset (noun): The larger set that contains the subset.
  • Example: The set of all real numbers is the superset for the set of integers.

Synonyms

• Portion
• Part
• Division
• Section
• Subgroup

Antonyms

• Superset

Học thuật

Noun

1. a set whose members are members of another set; a set contained within another set