# Bowtie

## The Mathematical Symbol "Bowtie (⋈)"

homesitemapsymbolsbowtie

The ⋈ Symbol in Mathematics: Natural Join and Relations

The ⋈ symbol in mathematics, resembling a bowtie, is not as widely recognized as symbols like "+" or "-". However, in specific domains, especially within relational database theory and certain areas of set theory, it plays an essential role. This lesson covers two primary contexts where the ⋈ symbol finds its application, providing two illustrative examples for each.

## 1. Relational Database Theory

In relational databases, the ⋈ symbol represents the "natural join" of two tables. It's a binary operation that combines two tables based on common attributes.

• Example 1: If there are two tables, Employees and Departments, with a common attribute DepartmentID, the natural join of these tables can be expressed as: Employees ⋈ Departments. This operation results in a combined table including rows where the DepartmentID matches in both original tables.
• Example 2: For tables Orders and Customers having a shared attribute CustomerID, the expression Orders ⋈ Customers denotes the natural join, merging order details with respective customer information based on the CustomerID.

## 2. Set Theory and Relations

In certain areas of set theory and relations, the ⋈ symbol represents a specific kind of product or combination of relations.

• Example 1: Given two relations $$R$$ and $$S$$ on sets $$A$$ and $$B$$ respectively, the expression $$R ⋈ S$$ can symbolize a specific type of product or composite relation between the two.
• Example 2: If $$R$$ is a relation from set $$A$$ to $$B$$ and $$S$$ is a relation from $$B$$ to $$C$$, then the composite relation $$R ⋈ S$$ might denote pairs from $$A$$ to $$C$$ that can be formed by combining pairs in $$R$$ and $$S$$.

In summary, while the ⋈ symbol might not be an everyday mathematical notation for many, its significance in relational database theory and set theoretic relations is undeniable. Recognizing its meaning in these contexts can lead to deeper insights into the structures and operations discussed.

## Are You Good at Mathematical Symbols?

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## Codes for the ⋈ Symbol

 The Symbol ⋈ Alt Code Alt 8904 HTML Code ⋈ HTML Entity ⋈ CSS Code \22C8 Hex Code ⋈ Unicode U+22C8

## 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 8904. 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: &#8904;</b>My symbol: ⋈

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

HTML TextOutput
<b>My symbol: &bowtie;</b>My symbol: ⋈

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

CSS and HTML TextOutput
<style>
span:after {
content: "\22C8";}
</style>
<span>My symbol:</span>
My symbol: ⋈

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

HTML TextOutput
<b>My symbol: &#x22C8;</b>My symbol: ⋈
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x22C8 to place the ⋈ symbol on your canvas. For example:
JavaScript Text
const x = "0x"+"E9"
ctx.fillText(String.fromCodePoint(x), 5, 5);
Output

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

The Unicode for ⋈ is U+22C8. 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:
TypeOutput
22C8
[Hold down Alt]
[Press x]

(The 22C8 turns into ⋈. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u22C8. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u22C8"
document.write("My symbol: " + str)
My symbol: ⋈

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## More about Mathematical Symbols

Mathematics is a universal language that is used to describe and understand the intricacies of the universe. At the heart of this language are symbols, concise representations that convey specific meanings and ideas.

Just as letters come together to form words in spoken languages, mathematical symbols combine to form expressions and equations, encapsulating intricate ideas in a compact form. The history of these symbols is as varied as their meanings; some have been in use for centuries while others have been introduced more recently to describe new discoveries and concepts. Whether you are a student, educator, researcher, or simply curious, this list of mathematical symbols will serve as a guide, shedding light on their meanings, origins, and applications.

From the simple plus and minus signs to the more esoteric and complex, each symbol has its unique story and significance.

## More Symbols

Full List of Mathematical Symbols