set (in mathematics) containing no elements
{\displaystyle \emptyset }
In mathematics, the empty set or void set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure … Wikipedia
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Wikipedia
en.wikipedia.org › wiki › Empty_set
Empty set - Wikipedia
February 4, 2026 - U+2205 ∅ EMPTY SET. It can be coded in HTML as ∅ and as ∅ or as ∅. It can be coded in LaTeX as \varnothing. The symbol
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Wumbo
wumbo.net › symbols › empty-set
Empty Set Symbol (∅)
Empty set symbol. ... The 0 (zero) symbol is used in math to represent the number zero or nothing.
Discussions

What letter is the empty set symbol ∅ to you?
Those are all distinct symbols, as you can see here: Greek Phi — capital: Φ, lowercase: φ/ϕ "slashed O" — capital: Ø, lowercase: ⊘ Empty set: ∅ More on reddit.com
🌐 r/mathematics
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March 30, 2024
elementary set theory - Which symbol should be used for an empty set? - Mathematics Stack Exchange
Do you know a source for the statement, ... this symbol? ... $\begingroup$ Well, I'd say the macro name \emptyset should be a dead giveaway. BTW, is it intentional that you linked to the English Wikipedia article, although you speak about the German one? $\endgroup$ ... $\begingroup$ I think that $\emptyset$ vs. $\varnothing$ is a typographical preference. I have seen both used in set theory books and papers. I am inclined towards $\varnothing$ personally. This is similar to $\mathbb R$ ... More on math.stackexchange.com
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August 21, 2012
elementary set theory - Name of symbol of null set. - Mathematics Stack Exchange
Note also, that the Wikipedia article says that the symbol is not to be confused with the Greek letter $\phi$ or $\Phi$. ... $\begingroup$ OK in mathematics we call it by empty set not by its Danish language name. More on math.stackexchange.com
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September 17, 2015
What does the hollow dot mean?

In a lot of contexts, the hollow dot would mean function composition, but I'm inclined to think this is a typographical issue. The problem reads like somebody was trying to write up an equation that they want you to solve, and the symbols aren't being displayed correctly.

Can I take a wild guess and ask if this problem was presented via some sort of web-assignment system? Like, say, MyMathLab?

Try this: replace the commas with plus signs, and replace the hollow dot with an equals sign. Does the result look like the sort of problem you've been studying? If so, I would suggest trying to solve that, then bringing the issue to your instructor's attention-- if you're having this issue, so are others, and your instructor needs to be aware of this.

Best of luck!

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People also ask

What is a non-empty set?

Any set with at least one element is a non-empty set.

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splashlearn.com
splashlearn.com › home
Empty Set: Definition, Properties, Notation, Symbol, Examples
Why is an empty set called a set?

We know that a set is a collection of well-defined objects. However, if we define a set using conditions that are not satisfied by any real number, the set will have no elements. If you subtract a set from itself, you will get A - A, which is a set with nothing in it. If the intersection of two sets A and B, since it is possible that A and B have no elements in common (for example, if A is the even integers and B is the odd integers). To define such sets, you need the empty set.

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splashlearn.com
splashlearn.com › home
Empty Set: Definition, Properties, Notation, Symbol, Examples
What is an example of the empty set?
The empty set is the set that contains zero elements. A usual set contains elements: A={1, 2, 3} is a non-empty set. An empty set would look like: {}. There are no elements inside the brackets so this set is "empty".
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study.com
study.com › courses › math courses › precalculus: high school
Empty Set | Definition & Symbol - Lesson | Study.com
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Wikipedia
en.wikipedia.org › wiki › Null_sign
Null sign - Wikipedia
1 week ago - The null sign (∅) is a symbol often used in mathematics for denoting the empty set. The same letter in linguistics represents zero, the lack of an element. It is commonly used in phonology, morphology, and syntax. The symbol ∅ is available at Unicode point U+2205.
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Reddit
reddit.com › r/mathematics › what letter is the empty set symbol ∅ to you?
r/mathematics on Reddit: What letter is the empty set symbol ∅ to you?
March 30, 2024 - So, the empty set symbol ∅ its own thing, it's not phi, it's not a slashed O... it's an empty set symbol. It was conceptualized independently of those characters so it's quite silly to assume that it's a "variant" of them just because it superficially resembles them. Another point to add is that Unicode treats different glyphs of the same grapheme differently in mathematical contexts if those different glyphs have a semantic distinction (e.g.
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Study.com
study.com › courses › math courses › precalculus: high school
Empty Set | Definition & Symbol - Lesson | Study.com
September 1, 2015 - An empty set would look like: {}. There are no elements inside the brackets so this set is "empty". The phrase "no solution" means that an equation or inequality does not have a solution. Since 0 would be a solution, these are not the same thing. Having no solution means no value satisfies the equation or inequality not that zero is a solution. ... There are many different symbols that arise in discrete math.
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SplashLearn
splashlearn.com › home
Empty Set: Definition, Properties, Notation, Symbol, Examples
February 5, 2024 - As mentioned earlier, we can represent an empty set either with a special symbol or with the conventional curly brackets { } with no elements inside.
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Cuemath
cuemath.com › algebra › empty-set
Empty Set - Definitions, Properties, Examples | Null Set
A set that does not contain any element is called an empty set or a null set. An empty set is denoted using the symbol ''. It is read as 'phi'. Example: Set X = {}. It is also called a void set or null set.
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Mathematics Monster
mathematics-monster.com › symbols › Empty-Set.html
The "Empty Set (∅)" Symbol - Mathematics Monster
The ∅ symbol is used to represent a set that has no members or elements. In set theory, an essential branch of mathematical logic and foundational mathematics, the concept of the empty set plays a crucial role as it provides a basis for building ...
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Quora
quora.com › What-is-the-name-of-the-symbol-Which-we-use-for-empty-set-in-mathematics
What is the name of the symbol ∅ ? Which we use for empty set in mathematics. - Quora
[ 1 ] It can be coded in HTML as ∅ and as ∅ or as ∅ . It can be coded in LaTeX as \varnothing . Similar letters and symbols include the following: In mathematics, the null sign (∅) denotes the empty set .
Top answer
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I would say the following should be not too controversial:

  • and are typographical variants of the same mathematical symbol designating the empty set

  • The symbol was introduced by Bourbaki, was inspired by the Norwegian character Ø, but is a distinct character from it

  • The intention was most probably to create a symbol related to (zero), not to O (Oh), distinguished from it by striking it through. After all the empty set has all kinds of relations with the number , but none with the letter O. (By contrast big-Oh and little-o symbols derive from the word "order".)

  • The symbol has absolutely no relation (apart from appearance) with the lower-case Greek letter phi, with typographical variants and .

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There is a webpage where you can find mention of this: http://jeff560.tripod.com/set.html

Here's an extract

The null set symbol (Ø) first appeared in N. Bourbaki Éléments de mathématique Fasc.1: Les structures fondamentales de l'analyse; Liv.1: Theorie de ensembles. (Fascicule de resultants) (1939): "certaines propriétés... ne sont vraies pour aucun élément de E... la partie qu’elles définissent est appelée la partie vide de E, et designée par la notation Ø." (p. 4.)

André Weil (1906-1998) says in his autobiography that he was responsible for the symbol:

Wisely, we had decided to publish an installment establishing the system of notation for set theory, rather than wait for the detailed treatment that was to follow: it was high time to fix these notations once and for all, and indeed the ones we proposed, which introduced a number of modifications to the notations previously in use, met with general approval. Much later, my own part in these discussions earned me the respect of my daughter Nicolette, when she learned the symbol Ø for the empty set at school and I told her that I had been personally responsible for its adoption. The symbol came from the Norwegian alphabet, with which I alone among the Bourbaki group was familiar.

The citation above is from page 114 of André Weil's The Apprenticeship of a Mathematician, Birkhaeuser Verlag, Basel-Boston-Berlin, 1992. Translated from the French by Jennifer Gage. The citation was provided by Julio González Cabillón.

You should also note that Nicolas Bourbaki is a collective pseudonym for a group of French-speaking mathematicians.

Concerning your question, I remember one of my math professor telling us that in fact, it was a claim by both André Weil and Claude Chevalley, but I can't find the citation for Chevalley.


I've found also this lecture about history of math from a Canadian University (in French), where this issue is mentioned: http://www.mat.ulaval.ca/fileadmin/Cours/MAT-2500/Bourbaki.pdf

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BYJUS
byjus.com › maths › empty-set
Empty Set Definition
The set of natural numbers less than 1 is an empty set since the natural numbers start from 1, and hence, there will be no elements in the required set. ... In maths, the symbol Ø is used in set theory to represent the empty set.
Published   May 18, 2022
Views   31K
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CK-12 Foundation
ck12.org › all subjects › cbse math › sets and its types › what is an empty set in maths?
What is an empty set in maths? - Symbol & Definition | CK-12 Foundation
September 11, 2025 - In mathematics, an empty set, also known as a null set, is a set that contains no elements. It is denoted by the symbol @$\begin{align*}\emptyset\end{align*}@$ or by @$\begin{align*}\{\}\end{align*}@$. For example, the set of all integers that are both even and odd is an empty set, because ...
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Encyclopedia Britannica
britannica.com › science › null-set
Null set | mathematics | Britannica
In mathematics, the null set, also known as the empty set, is a set that contains no elements. It is symbolized by $\Lambda$ or $\emptyset$. The term "null" itself originates from Latin and means "not any". In mathematics, it signifies a complete absence, such as a set with zero members.
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VEDANTU
vedantu.com › maths › what does the empty set (∅) mean in mathematics?
Empty Set (∅) in Math: Meaning, Symbol, and Examples
February 17, 2026 - Although the symbols Ø (uppercase o-slash) and (empty set) look similar, only is the standard symbol for the empty set in mathematics.
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Wolfram MathWorld
mathworld.wolfram.com › EmptySet.html
Empty Set -- from Wolfram MathWorld
January 17, 2009 - The set containing no elements, commonly denoted emptyset or emptyset, the former of which is used in this work. These correspond to Wolfram Language and TeX characters summarized in the table below. symbol TeX Wolfram Language emptyset \varnothing \[Diameter] emptyset \emptyset \[EmptySet] Unfortunately, some authors use the notation 0 instead of emptyset for the empty set (Mendelson 1997).
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Quora
quora.com › What-is-the-name-of-the-symbol-used-for-expressing-empty-sets
What is the name of the symbol used for expressing empty sets? - Quora
Sign representing zero or empty set 6 The null sign (∅) is a symbol often used in mathematics for denoting the empty set . The same letter in linguistics represents zero , the lack of an element.
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Aphtech
uebmath.aphtech.org › lesson7.0
Lesson 7.0: Set Notation: Complements and Subsets
The symbol for a subset (contained in or equal to) ⊆, is the subset symbol with a horizontal line displayed beneath it. The symbol for contained in or equal to is three cells; dots four five six in the first cell, dots four five in the second cell, and dots one two six in the third cell. ... The empty or null set denoted by ∅, is also a subset of any given set.
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GeeksforGeeks
geeksforgeeks.org › mathematics › empty-set
Empty Set(Null Set): Definition, Notation, Properties, & Examples - GeeksforGeeks
October 29, 2025 - The multiplication of the provided sets is defined by the Cartesian product. Taking the cartesian product of any set with an empty/null set always yields an empty result. The explanation is obvious: the empty set includes no items. Mathematically expressed as: B x Φ = Φ; ∀ B