Set Symbols: Comprehensive List of Math Theory 

April 14, 2024
Mathematics is the language of the universe. There are many scientific equations and concepts that are based on mathematical expressions. Sets symbols have been a part of all civilizations and organized as a part of basic knowledge in every aspect of human intelligence and creative thought.
Name Symbol
set { }
such that |
not subset A⊄B
union A⋃B
subset A⊆B
proper subset / strict subset A⊂B
complement Ac
superset A⊇B
equality A=B
proper superset / strict super A⊃B
not superset A⊅B
cardinality |A|
power set P(A)
intersection A⋂B
element of, belongs to a∈A
not element of x∉A
relative complement A\B
symmetric difference AΔB
ordered pair (a,b)
cartesian product A×B
vertical bar |
aleph-null ℵ0
aleph-one ℵ1
empty set Ø
natural numbers / whole numbers ℕ0, ℕ1
integer numbers set
rational numbers set
real numbers set
complex numbers set

Sets are a mathematical object that include all possible objects having some common property and which can be defined by the property. The sets are represented by symbols or words, often written in italics.

Set Symbols

Set theory is one of the most important branches of mathematics and contains many powerful concepts.

 However, one great challenge in teaching and learning set theory is the overwhelming amount of terminology. 

There are terms such as element, subset, equal sets, cardinality, Ordinal numbers, sequences of sets, rational sets, etc. 

Intersection Symbol

The intersection symbol (∩) is called a "set-intersection" or "cap", and appears in Unicode as U+2227. It is used in mathematics to indicate the union of two sets . It also represents the first woman elected to serve on the US Supreme Court. 

The Double Intersection symbol (⋁) is used by chemists and organic chemists to represent a molecular orbital diagram.

Subset Symbol

Let’s talk about the symbol ⊂. Informally, we use it to express that one thing is included as a subset of another.. So for example, the set of natural numbers is a subset of the set of whole numbers.

Proper subset Symbol

A proper subset symbol is a type of mathematical notation used to denote elements of a set from within another set. 

A proper subset symbol is employed as opposed to listing the particular elements of a set for those situations where it is preferable not list all the subordinate elements, either because there are too many such elements or for ease of presentation.

Power set Symbol

You have already seen the power set symbol , a powerful set of symbols which consists of all the possible subsets of a given set: {}. 

As you have seen the factorial is simply represented with a factorial notation 5! = 5 x 4 x 3 x 2 x 1. 

The same thing applies for the power set: To compute its value we start with an ordered sequence of elements (or terms), and then we determine for each element whether it belongs in or not. 

Of course, this restricts to a selection of terms from the sequence, but this set contains unimaginably many combinations that are simply represented as .

Relative complement Symbol

Relative complement in set theory represents a particular binary relation in the set which is used to indicate the relative difference from the two elements of a pair. 

The relative complement of A with respect to B is denoted by A ∩ where |A| denotes the cardinal number of the set A and |B| denotes the cardinal number of the set B.D

Symmetric Difference Symbol

The symmetric difference symbol is one of the most useful symbols in mathematics. It is used in set theory, to be sure, but also in many other fields including logic and cryptography.

Cardinality Symbol

A cardinality symbol is another mathematical icon for set theory, and it has a variety of uses in information management. T

he symbol, which also appears in front of the name of the set, has a variety of uses: it can mean that something is finite; or it could also be used to denote that a set might be infinite.

Aleph-null Symbol

Aleph-null is a symbol used in computer science to represent the number of possible states of a system, especially in finite state machines. 

The term literally means "aleph-naught", from the first names of the Hebrew letters aleph and nought, but very briefly is commonly written as ℵ0 , the limit of the sequence formed by skipping successive integers.

Real Numbers Set Symbol

In set theory and its applications, the real numbers are constructed using a building block principle that starts with the rational numbers. 

They are constructed from the rational numbers in such a way that a set of real numbers having certain properties is an equivalence class of ratios of two rational numbers. 

The real numbers can thus be thought of as "the infinite-dimensional extension of the rational numbers

If you want see other symbol collection here is the page you should check

Related: Random Symbols Generator, Copy and Paste Symbols

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