# Element vs. Subset — What's the Difference?

Edited by Tayyaba Rehman — By Urooj Arif — Updated on May 13, 2024
An element is a single member of a set, whereas a subset is a collection of elements from a set that forms another set.

## Key Differences

An element refers to a single object or member within a set. For example, in the set {1, 2, 3}, each of the numbers 1, 2, and 3 is an element of this set. On the other hand, a subset includes any combination of these elements that itself forms a set. The subsets of {1, 2, 3} include {}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, and {1, 2, 3}.
Every set contains itself and the empty set as subsets. This means that for any set, at least two subsets can always be defined: the set itself and the empty set. In contrast, an element does not inherently contain other elements or sets; it is simply a single distinct member of a set.
The concept of an element is central to the definition of a set; a set is defined by the elements it contains. A subset, however, is a secondary concept that arises from taking any number of elements from an existing set, possibly including none, to form new sets.
Subsets can also include other subsets, forming a hierarchy or nested structure within the parent set. For example, the subset {2, 3} can be a part of larger subsets like {1, 2, 3}. However, an element like '3' does not contain other elements and does not form a hierarchy within a set.

## Comparison Chart

### Definition

A single member of a set.
A collection of elements that forms another set.

### Examples in set {1, 2, 3}

1, 2, 3
{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}

### Inherent structure

Singular; no subsets.
Can include multiple elements, including none (empty set).

### Relationship to original set

Member of the set.
Can be equal to or smaller than the original set.

## Compare with Definitions

#### Element

A distinct item in a mathematical or logical set.
An element in a matrix can be defined by its position.

#### Subset

A part of a set that is itself a set, possibly empty.
The empty set is a subset of every set.

#### Element

A point, idea, or part considered as part of a whole.
Trust is an essential element in the relationship.

#### Subset

A segment or portion of a set that holds some or all elements of the parent set.
The subset of prime numbers below 10 includes {2, 3, 5, 7}.

#### Element

A fundamental, essential, or irreducible constituent of a composite entity.

#### Subset

A collection derived from a larger set by including some or no elements.
{a, c} is a subset of {a, b, c, d}.

#### Element

Elements The basic assumptions or principles of a subject.

#### Subset

A set formed from any combination of elements from another set.
The set {1, 3} is a subset of {1, 2, 3, 4}.

#### Element

A member of a set.

#### Subset

In mathematics, a set that can be injected into another set without any exclusions.
All even numbers form a subset of the natural numbers.

#### Element

A point, line, or plane.

#### Subset

In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment). A is a subset of B may also be expressed as B includes (or contains) A or A is included (or contained) in B. The subset relation defines a partial order on sets.

#### Element

A part of a geometric configuration, such as an angle in a triangle.

#### Subset

A set contained within a set.

#### Element

The generatrix of a geometric figure.

#### Subset

A set A such that every element of A is also an element of S.
The set of integers is a subset of the set of real numbers.
The set $\lbrace a, b\rbrace$ is a both a subset and a proper subset of $\lbrace a, b, c\rbrace$ while the set $\lbrace a, b, c\rbrace$ is a subset of $\lbrace a, b, c\rbrace$ but not a proper subset of $\lbrace a, b, c\rbrace$.

#### Element

Any of the terms in the rectangular array of terms that constitute a matrix or determinant.

#### Subset

A group of things or people, all of which are in a specified larger group.
We asked a subset of the population of the town for their opinion.

#### Element

Chemistry & Physics A substance composed of atoms having an identical number of protons in each nucleus. Elements cannot be reduced to simpler substances by normal chemical means. See Periodic Table.

#### Subset

(transitive) To take a subset of.

#### Element

One of four substances, earth, air, fire, or water, formerly regarded as a fundamental constituent of the universe.

#### Subset

To extract only the portions of (a font) that are needed to display a particular document.

#### Element

(Electricity)The resistance wire in an electrical appliance such as a heater or an oven.

#### Subset

A set whose members are members of another set; a set contained within another set

#### Element

Elements The forces that constitute the weather, especially severe or inclement weather:outside paint that had been damaged by the elements.

#### Element

An environment naturally suited to or associated with an individual:He is in his element when traveling. The business world is her element.

#### Element

A distinct group within a larger community:the dissident element on campus.

#### Element

A ground unit in an air force comparable to a platoon.

#### Element

A unit of an air force equal to two or three aircraft.

#### Element

Elements The bread and wine of the Eucharist.

#### Element

One of the simplest or essential parts or principles of which anything consists, or upon which the constitution or fundamental powers of anything are based.
Letters are the elements of written language.

#### Element

(chemistry) Any one of the simplest chemical substances that cannot be decomposed in a chemical reaction or by any chemical means and made up of atoms all having the same number of protons.

#### Element

One of the four basic building blocks of matter in theories of ancient philosophers and alchemists: water, earth, fire, and air.

#### Element

A basic, simple substance out of which something is made, raw material.

#### Element

(legal) A required aspect or component of a cause of action. A deed is regarded as a violation of law only if each element can be proved.

#### Element

(set theory) One of the objects in a set.

#### Element

(mathematics) One of the entries of a matrix.

#### Element

Any of the teeth of a zip fastener.

#### Element

A small part of the whole.
An element of the picture

#### Element

A small but present amount of a quality, a hint.
An element of doubt

#### Element

A factor, one of the conditions contributing to a result.

#### Element

(obsolete) The sky.

#### Element

(obsolete) Any one of the heavenly spheres believed to carry the celestial bodies.

#### Element

Atmospheric forces such as strong winds and rains.
Exposed to the elements

#### Element

A place or state of being that an individual or object is best suited to.
To be in one's element

#### Element

The bread and wine taken at Holy Communion.

#### Element

A group of people within a larger group having a particular common characteristic.
You sometimes find the hooligan element at football matches.

#### Element

(in the plural only) The basic principles of a field of knowledge, basics, fundamentals, rudiments.

#### Element

A component in electrical equipment, often in the form of a coil, having a high resistance, thereby generating heat when a current is passed through it.
The element in this electric kettle can heat the water in under a minute.

#### Element

(mathematics) An infinitesimal interval of a quantity, a differential.
The element of area in Cartesian coordinates is dx dy.

#### Element

(astronomy) An orbital element; one of the parameters needed to uniquely specify a particular orbit.

#### Element

(computing) One of the conceptual objects in a markup language, usually represented in text by tags.

#### Element

(obsolete) To compound of elements.

#### Element

(obsolete) To constitute and be the elements of.

#### Element

One of the simplest or essential parts or principles of which anything consists, or upon which the constitution or fundamental powers of anything are based.

#### Element

One of the ultimate, undecomposable constituents of any kind of matter. Specifically: (Chem.) A substance which cannot be decomposed into different kinds of matter by any means at present employed; as, the elements of water are oxygen and hydrogen.

#### Element

One of the ultimate parts which are variously combined in anything; as, letters are the elements of written language; hence, also, a simple portion of that which is complex, as a shaft, lever, wheel, or any simple part in a machine; one of the essential ingredients of any mixture; a constituent part; as, quartz, feldspar, and mica are the elements of granite.
The simplicity which is so large an element in a noble nature was laughed to scorn.

#### Element

One out of several parts combined in a system of aggregation, when each is of the nature of the whole; as, a single cell is an element of the honeycomb.

#### Element

One of the simplest essential parts, more commonly called cells, of which animal and vegetable organisms, or their tissues and organs, are composed.

#### Element

An infinitesimal part of anything of the same nature as the entire magnitude considered; as, in a solid an element may be the infinitesimal portion between any two planes that are separated an indefinitely small distance. In the calculus, element is sometimes used as synonymous with differential.

#### Element

One of the necessary data or values upon which a system of calculations depends, or general conclusions are based; as, the elements of a planet's orbit.

#### Element

The simplest or fundamental principles of any system in philosophy, science, or art; rudiments; as, the elements of geometry, or of music.

#### Element

Any outline or sketch, regarded as containing the fundamental ideas or features of the thing in question; as, the elements of a plan.

#### Element

One of the simple substances, as supposed by the ancient philosophers; one of the imaginary principles of matter.
Of elementsThe grosser feeds the purer: Earth the Sea;Earth and the Sea feed Air; the Air those FiresEthereal.
Does not our life consist of the four elements?
And the complexion of the element [i. e.,the sky or air]In favor's like the work we have in hand,Most bloody, fiery, and most terrible.
About twelve ounces [of food], with mere element for drink.
They show that they are out of their element.

#### Element

The conditions and movements of the air.

#### Element

The whole material composing the world.
The elements shall melt with fervent heat.

#### Element

The bread and wine used in the eucharist or Lord's supper.

#### Element

To compound of elements or first principles.

#### Element

To constitute; to make up with elements.
His very soul was elemented of nothing but sadness.

#### Element

An abstract part of something;
Jealousy was a component of his character
Two constituents of a musical composition are melody and harmony
The grammatical elements of a sentence
A key factor in her success
Humor: an effective ingredient of a speech

#### Element

Any of the more than 100 known substances (of which 92 occur naturally) that cannot be separated into simpler substances and that singly or in combination constitute all matter

#### Element

An artifact that is one of the individual parts of which a composite entity is made up; especially a part that can be separated from or attached to a system;
Spare components for cars
A component or constituent element of a system

#### Element

One of four substances thought in ancient and medieval cosmology to constitute the physical universe;
The alchemists believed that there were four elements

#### Element

The most favorable environment for a plant or animal;
Water is the element of fishes

#### Element

The situation in which you are happiest and most effective;

#### Element

A straight line that generates a cylinder or cone

#### Element

A basic constituent that can’t be simplified further within the theory of sets.
In the set {a, b, c}, 'a' is an element.

#### Element

Any one member or distinct part of a set.
The number 5 is an element of the set of positive integers.

#### Element

A particular object in a collection.
Each puzzle piece is an element of the puzzle set.

## Common Curiosities

#### Is the empty set a subset of every set?

Yes, the empty set is universally considered a subset of every set.

#### How are subsets formed?

Subsets are formed by selecting any combination of elements from a set, including none (empty set).

#### Can an element be a subset?

No, an element is not a subset; it is a single unit within a set.

#### What does it mean for a set to be a subset of another set?

A set is a subset of another if all elements of the former are contained within the latter.

#### What is the minimum number of subsets a set can have?

Every set has at least two subsets: the set itself and the empty set.

#### What is a singleton in set theory?

A singleton is a set containing exactly one element, thus also a subset.

The symbol

#### ⊆

⊆ denotes that one set is a subset of another.

#### How do you determine if a collection is an element or a subset?

If the collection contains more than one item or no items, it is a subset; if it is a single, distinct item, it is an element.

#### ∈

∈ is used to denote that an object is an element of a set.

#### Are all elements of a set also subsets?

No, only the singletons (sets containing exactly one element) and the set itself are considered subsets.

#### What is an element in a set?

An element is a single, indivisible member of a set.

#### How is the concept of subsets useful in mathematics?

The concept of subsets is fundamental in various mathematical disciplines, facilitating discussions on relations, functions, and more.

#### Can a subset be equal to the original set?

Yes, a subset can be equal to the original set if it includes all elements of that set.

The symbol

#### Is every combination of elements in a set a subset?

Yes, every combination of elements, including no elements (empty set), forms a subset.

#### Can subsets contain other subsets?

Yes, subsets can contain other subsets, forming a nested structure.

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