Wumbo
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Union Symbol (∪)
The set union symbol (∪) is used in math to represent the union operator in set theory.
Wikipedia
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Union (set theory) - Wikipedia
1 month ago - In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other. A nullary union refers to a union of zero ( ... For explanation of the symbols ...
set theory - What does the union symbol (∪) before the set builder notation mean? - Mathematics Stack Exchange
Added: For your exercise, you just want to show the two sets are equal, so as usual, show they are subsets of each other. So show any natural number is in that union, and then show that any member of that union is in fact a natural number · Second addendum: Technically the author should have written · $$\bigcup_{x\in \mathbb ... More on math.stackexchange.com
What's this union symbol doing without anything on its left?
The "big union" symbol is used to denote a union of a large (or even infinite) number of elements. This notation tells us to successively apply the union operator to all elements which meet some criteria. Let's use a different example to illustrate what's going on. Suppose we wanted to know what's the union of all subsets of the positive integers with cardinality of at least 3? Well we could write: {1, 2, 3} ∪ {1, 2, 3, 4} ∪ {1, 2, 3, 4, 5} ∪ ... ∪ {17, 18, 19} ∪ ... But since there are infinitely many such subsets we can't possibly write them all. But what we could do is use the "big union" symbol with a subscript of: X ∈ ℤ+, |X| >= 3 More on reddit.com
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March 25, 2019elementary set theory - Union-like symbol meaning - Mathematics Stack Exchange
This symbol is write the summation symbol, and represents a shorthand for union of many sets. In particular, $$\bigcup_{i=0}^nA_i = A_1\cup A_2\cup \cdots A_n$$ In your case, that means the union of all sets $S_i$ where $i$ is the element of $\mathcal I$. More on math.stackexchange.com
What does ∪ mean?
Your right Union symbol simply means Combining between Domain A and Domain B Or function A and B or range A or B For example let’s say we have this set of numbers A= [1,2,3,4] B= [ 5,6,7,8] By using the Union symbol We are simply Combining set A and B making them One set instead of two So A ∪ B = [1,2,3,4,5,6,7,8] For intersection it’s a little bit different It means to take both common elements from both sets of A and B and make it in one set For example A= [ 2,4,6,8 ] B= [ 1,2,6,8] By using intersection symbol we take only the common numbers in both A and B and put it in one set So , A∩B = [2,6,8] More on reddit.com
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February 17, 2024What does union mean in math sets?
The union of two or more sets is the collection of elements belonging to all of the sets. That is, if A and B are sets, then the union of A and B is the set of elements in A or in B.
study.com
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Union of Sets in Math | Definition, Symbol & Applications - Lesson ...
What is union of sets with examples?
Consider two sets: A = {1, 2, 3} and B = {4, 5, 6}. The union of A and B is the collection of elements from both sets: A U B = { 1, 2, 3, 4, 5, 6}.
study.com
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Union of Sets in Math | Definition, Symbol & Applications - Lesson ...
What does the U mean in math?
The U in math is the symbol used to represent the union of two or more sets. So, if A and B are sets, then A U B is the union of these sets.
study.com
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Union of Sets in Math | Definition, Symbol & Applications - Lesson ...
Videos
11:49
Intersection of Sets, Union of Sets and Venn Diagrams - YouTube
00:49
How to insert Union symbol in Word - YouTube
02:45
What is a Union? (Set Theory) - YouTube
Universal set and absolute complement (video)
05:40
Sets: Union and Intersection - YouTube
Intersection and union of sets (video)
Study.com
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Union of Sets in Math | Definition, Symbol & Applications - Lesson | Study.com
November 9, 2015 - This symbol is pronounced as or when used in a mathematical statement. Here is an example showing this union symbol: Consider the example from the previous section concerning ice cream flavors. If the set of all people who bought vanilla is V and the set of all people who bought chocolate is C, then the set of those who bought both chocolate and vanilla (the union of the two sets) is {eq}V \cup C {/eq}.
Piliapp
piliapp.com › symbols › union
∪ Union Symbol - PiliApp
The Union Symbol, symbolized by ∪, is used in set theory to denote the union of two or more sets. A union contains all distinct elements from all the sets under consideration. The Union Symbol (∪) has applications in multiple disciplines: Mathematics: Widely used in set theory, algebra, ...
Cuemath
cuemath.com › algebra › union-of-sets
Union of Sets - Formula, Meaning, Examples | Finding a Union
The union of two given sets is the set that contains all the elements present in one/both sets. The symbol for the union of sets is "∪''. Learn more about the union of sets with concepts, definitions, properties, and examples.
Mathematics Monster
mathematics-monster.com › symbols › Union.html
The "Union (∪)" Symbol - Mathematics Monster
Union is used to denote set union. Codes: Alt 8746, HTML ∪, hex U+222A.
Statistics LibreTexts
stats.libretexts.org › bookshelves › introductory statistics › support course for elementary statistics › sets
The Union and Intersection of Two Sets - Statistics LibreTexts
April 9, 2022 - Write this in set notation as the union of two sets and then write out this union. ... First, let A be the set of the number of windows that represents "fewer than 6 windows". This set includes all the numbers from 0 through 5: ... Next, let B be the set of the number of windows that represents "has a dozen windows". This is just the set that contains the single number 12: ... An element is in the intersection of two sets if it is in the first set and it is in the second set. The symbol we use for the intersection is \(\cap\).
RapidTables
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Set symbols of set theory (Ø,U,{},∈,...)
Set symbols of set theory and probability with name and definition: set, subset, union, intersection, element, cardinality, empty set, natural/real/complex number set
Oreate AI
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Understanding the Union Symbol in Mathematics - Oreate AI Blog
January 15, 2026 - For instance, if you have Set A containing {1, 2} and Set B containing {2, 3}, their union—written as A ∪ B—would yield {1, 2, 3}. This is because while both sets share the number '2', it only appears once in the combined result.
Top answer 1 of 4
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In a set theory development of the natural numbers, what we do is we start with nothing but sets and then build structures within that mimic our knowledge of numbers and operations on them. The standard construction for the natural numbers is to set
and then inductively define each following natural number by the successor function 
which gives the next number after 
as
So 
, 
, etc.
Note in this construction the only objects are the empty set and sets built from the empty set, the numbers are just names we assign to certain configurations of the sets. In this configuration, it is true that any natural number is just the set of all the previous numbers
Thus it makes the sense to take the union of the numbers because numbers are just names for special sets. And when you take the union of all of them, you get all natural numbers.
Added: For your exercise, you just want to show the two sets are equal, so as usual, show they are subsets of each other. So show any natural number is in that union, and then show that any member of that union is in fact a natural number
Second addendum: Technically the author should have written
but when the context of the index set is obvious, we often do abuse of notation and skip writing the index set and go straight to
2 of 4
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The notation is not mysterious and is not “technically wrong” or “abusive” as others commented. You find it in several books; I learned it in the appendix of Kelley's book “General Topology”.
If 
is a set, then
For instance, if 
, then 
.
The book you link is not very consistent in notation, I should say.
In the “almost formal” set theory that's developed in the book, everything is a set. And the natural numbers are defined recursively by
and collecting what's obtained in this way in the set 
. Let's see what happens when the union is applied to 
instead of 
:
With 
we get
There seems to be a pattern. And indeed there is: if 
is a natural number and 
, then 
. Since, by definition,
you have that, when 
which you can prove by induction. It follows that
The notation 
is justified by a specific axiom of set theory: the axiom of union states that for any 
there exists 
such that, for every 
, there is 
with 
(probably not the same notation of your book). Using specification, we can isolate from that (possibly big) set the one that we need to use and denote it as shown above.
The “binary union” 
is defined to be 
.
CK-12 Foundation
ck12.org › all subjects › cbse math › venn diagrams and operations of sets › what does the union symbol (∪) mean in a venn diagram?
What does the union symbol (∪) mean in a Venn Diagram? - Examples, Symbol, & Definition | CK-12 Foundation
September 11, 2025 - If we have two sets @$\begin{align*}A\end{align*}@$ and @$\begin{align*}B,\end{align*}@$ the union of @$\begin{align*}A\end{align*}@$ and @$\begin{align*}B\end{align*}@$ is denoted by @$\begin{align*}A ∪ B\end{align*}@$ and it contains all the elements that are in @$\begin{align*}A,\end{align*}@$ ...
Math.net
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Union - Math.net
Given that A and B are subsets of the universal set 𝕌, this relationship can be seen in the figure below: The intersection of A and B, A ∩ B, is shaded in red. Its complement, (A ∩ B)C is shaded in grey. The union of the complements of A and B, AC ∪ BC, is also shaded in grey.
CK-12 Foundation
ck12.org › all subjects › cbse math › venn diagrams and operations of sets › what is the notation for the union of sets?
What is the notation for the Union of Sets? - Symbol & Definition | CK-12 Foundation
September 11, 2025 - If we have two sets @$\begin{align*}A\end{align*}@$ and @$\begin{align*}B,\end{align*}@$ the union of @$\begin{align*}A\end{align*}@$ and @$\begin{align*}B\end{align*}@$ is denoted by @$\begin{align*}A ∪ B\end{align*}@$ and it contains all the elements that are in @$\begin{align*}A,\end{align*}@$ ...
Expii
expii.com › t › union-of-sets-definition-examples-4303
Union of Sets - Definition & Examples - Expii
The union of sets includes every element from every set in the union. The union symbol ∪ means "or". The union looks for a number in one set or the other.
Mathspace
mathspace.co › textbooks › syllabuses › Syllabus-467 › topics › Topic-8760 › subtopics › Subtopic-116087
Union and intersection of sets | Grade 12 Math | Ontario 12 Mathematics of Data Management (MDM4U) | Mathspace
Mathematically we write the intersection of sets using the intersection symbol, $\cap$∩. We interpret the intersection of $A$A and $B$B, $A\cap B$A∩B to be what appears in both set $A$A and set $B$B.
Encyclopedia Britannica
britannica.com › philosophy & religion › philosophical issues
Set theory - Operations, Elements, Relations | Britannica
2 weeks ago - Set theory - Operations, Elements, Relations: The symbol ∪ is employed to denote the union of two sets. Thus, the set A ∪ B—read “A union B” or “the union of A and B”—is defined as the set that consists of all elements belonging ...
Reddit
reddit.com › r/askmath › what's this union symbol doing without anything on its left?
r/askmath on Reddit: What's this union symbol doing without anything on its left?
March 25, 2019 - The X at the end represent the sets being "unioned". The whole construction could be worded in plain English as: ... It's exactly the same usage as a big sigma. You need an index, and a summand.
Quora
quora.com › What-is-the-U-and-upside-down-U-in-math
What is the U and upside down U in math? - Quora
To summarize: - U (∪) represents the union of two sets, combining all elements without duplication. - Upside-Down U (∩) represents the intersection of two sets, finding the common elements.
Lumen Learning
courses.lumenlearning.com › mathforliberalartscorequisite › chapter › union-intersection-and-complement
Union, Intersection, and Complement | Mathematics for the Liberal Arts Corequisite
The intersection symbol looks a little like a big lower-case n, for in-tersect ... The union contains all the elements in either set: A ⋃ B = {red, green, blue, yellow, orange} Notice we only list red once.
Top answer 1 of 4
4
It is a union symbol. It is the union of all sets $S_i$, as $i$ ranges over all elements of the index set $I$.
$$\bigcup_{i\in I} S_i =\Bigl\{x\,\Bigm|\, \text{there exists }i\in I\text{ such that }x\in S_i\Bigr\}.$$
The symbol you describe is a special case, $$A_1\cup A_2 = \bigcup_{i\in\{1,2\}} A_i.$$
2 of 4
2
It is the union symbol. In this context, it is the union of all sets $S_i$, with $i\in I$.