The Mathematical Symbol "N-Ary Union (⋃)"

Understanding the "N-Ary Union" Symbol (⋃)

The ⋃ symbol, commonly referred to as the "N-Ary Union", is widely used in the field of set theory and mathematics. This article aims to shed light on the significance of this symbol and its applications by providing examples.

Meaning of ⋃

In set theory, the ⋃ symbol represents the union of multiple sets. Rather than the conventional binary union (two sets at a time), the N-Ary union allows for a union of any number of sets, thereby serving as a generalization.

Example 1: Combining Multiple Sets

Consider three sets \( A \), \( B \), and \( C \). The N-Ary Union of these sets can be expressed as: \[ A ⋃ B ⋃ C \]

Example 2: Representing Universal Sets

If you have a universal set \( U \) consisting of multiple smaller sets, the entire collection can be represented using the ⋃ symbol: \[ U = A_1 ⋃ A_2 ⋃ ... ⋃ A_n \]

Applications of ⋃

The ⋃ symbol is crucial in various contexts:

  • Mathematics: Primarily in set theory for representing the union of multiple sets.
  • Computer Science: Utilized in algorithms and data structures when dealing with collection types and their union operations.
  • Logic: In some contexts, it represents the logical OR operation for multiple statements or conditions.

In summary, the ⋃ symbol offers a comprehensive way to denote the union of several sets, making it a valuable tool in mathematics and related fields.

Mathematical symbol 'N-Ary Union'

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Codes for the ⋃ Symbol

The Symbol
Alt CodeAlt 8899
HTML Code⋃
HTML Entity⋃
CSS Code\22C3
Hex Code⋃

How To Insert the ⋃ Symbol

(Method 1) Copy and paste the symbol.

The easiest way to get the ⋃ symbol is to copy and paste it into your document.

Bear in mind that this is a UTF-8 encoded character. It must be encoded as UTF-8 at all stages (copying, replacing, editing, pasting), otherwise it will render as random characters or the dreaded �.

(Method 2) Use the "Alt Code."

If you have a keyboard with a numeric pad, you can use this method. Simply hold down the Alt key and type 8899. When you lift the Alt key, the symbol appears. ("Num Lock" must be on.)

(Method 3) Use the HTML Decimal Code (for webpages).

HTML TextOutput
<b>My symbol: &#8899;</b>My symbol: ⋃

(Method 4) Use the HTML Entity Code (for webpages).

HTML TextOutput
<b>My symbol: &xcup;</b>My symbol: ⋃

(Method 5) Use the CSS Code (for webpages).

CSS and HTML TextOutput
span:after {
content: "\22C3";}
<span>My symbol:</span>
My symbol: ⋃

(Method 6) Use the HTML Hex Code (for webpages and HTML canvas).

HTML TextOutput
<b>My symbol: &#x22C3;</b>My symbol: ⋃
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x22C3 to place the ⋃ symbol on your canvas. For example:
JavaScript Text
const x = "0x"+"E9"
ctx.fillText(String.fromCodePoint(x), 5, 5);

(Method 7) Use the Unicode (for various, e.g. Microsoft Office, JavaScript, Perl).

The Unicode for ⋃ is U+22C3. The important part is the hexadecimal number after the U+, which is used in various formats. For example, in Microsoft Office applications (e.g. Word, PowerPoint), do the following:
[Hold down Alt]
[Press x]

(The 22C3 turns into ⋃. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u22C3. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u22C3"
document.write("My symbol: " + str)
My symbol: ⋃