Element vs. Subset — What's the Difference?

A distinct item in a mathematical or logical set.

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

A point, idea, or part considered as part of a whole.

A segment or portion of a set that holds some or all elements of the parent set.

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

A collection derived from a larger set by including some or no elements.

Elements The basic assumptions or principles of a subject.

A set formed from any combination of elements from another set.

A member of a set.

In mathematics, a set that can be injected into another set without any exclusions.

A point, line, or plane.

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.

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

A set contained within a set.

The generatrix of a geometric figure.

A set A such that every element of A is also an element of S.

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

A group of things or people, all of which are in a specified larger group.

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.

(transitive) To take a subset of.

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

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

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

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

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

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

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

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

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

Elements The bread and wine of the Eucharist.

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.

(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.

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

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

(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.

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

(mathematics) One of the entries of a matrix.

Any of the teeth of a zip fastener.

A small part of the whole.

A small but present amount of a quality, a hint.

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

(obsolete) The sky.

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

Atmospheric forces such as strong winds and rains.

A place or state of being that an individual or object is best suited to.

The bread and wine taken at Holy Communion.

A group of people within a larger group having a particular common characteristic.

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

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.

(mathematics) An infinitesimal interval of a quantity, a differential.

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

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

(obsolete) To compound of elements.

(obsolete) To constitute and be the elements of.

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.

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.

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.

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.

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

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.

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.

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

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

One of the simple substances, as supposed by the ancient philosophers; one of the imaginary principles of matter.

The conditions and movements of the air.

The whole material composing the world.

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

To compound of elements or first principles.

To constitute; to make up with elements.

An abstract part of something;

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

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;

One of four substances thought in ancient and medieval cosmology to constitute the physical universe;

The most favorable environment for a plant or animal;

The situation in which you are happiest and most effective;

A straight line that generates a cylinder or cone

A basic constituent that can’t be simplified further within the theory of sets.

Any one member or distinct part of a set.

A particular object in a collection.

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

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

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

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

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

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

The symbol

⊆ denotes that one set is a subset of another.

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.

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

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

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

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

The symbol

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

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