Contains with Overbar

The Mathematical Symbol "Contains with Overbar (⋽)"

The ⋽ Symbol in Mathematics: Contains with Overbar

In the complex world of mathematical notations, the ⋽ symbol, or "Contains with Overbar", holds a specific place in set theory and group theory. This short lesson covers its primary use and present some illustrative examples for a clearer understanding.

Usage

The ⋽ symbol is used to show that a specific element or set is not a left coset of another set or subgroup within a given group.

Examples

• Example 1: In the context of group theory:
  Given a group \( G \) and a subgroup \( H \), if an element \( a \) in \( G \) does not form a left coset of \( H \) in \( G \), then we represent this as \( a ⋽ H \).
• Example 2: Using set notation:
  If we have a set \( S \) and a subset \( T \), and a particular subset \( U \) does not form a left coset relative to \( T \), we can represent it as \( U ⋽ T \).

In summary, the ⋽ symbol serves as a concise notation to express that a specific element or set does not form a left coset relative to another set or subgroup. Its recognition is essential for deciphering intricate relations in set or group structures.

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Codes for the ⋽ Symbol

The Symbol	⋽	copy
Alt Code	Alt 8957	copy
HTML Code	⋽	copy
HTML Entity	⋽	copy
CSS Code	\22FD	copy
Hex Code	⋽	copy
Unicode	U+22FD	copy

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 8957. When you lift the Alt key, the symbol appears. ("Num Lock" must be on.)

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

HTML Text	Output
<b>My symbol: &#8957;</b>	My symbol: ⋽

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

HTML Text	Output
<b>My symbol: &notnivc;</b>	My symbol: ⋽

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

CSS and HTML Text	Output
<style> span:after { content: "\22FD";} </style> <span>My symbol:</span>	My symbol: ⋽

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

HTML Text	Output
<b>My symbol: &#x22FD;</b>	My symbol: ⋽

On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x22FD 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+22FD. 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:

Type	Output
22FD [Hold down Alt] [Press x]	⋽ (The 22FD turns into ⋽. Note that you can omit any leading zeros.)

In JavaScript, the syntax is \uXXXX. So, our example would be \u22FD. (Note that the format is 4 hexadecimal characters.)

JavaScript Text	Output
let str = "\u22FD" document.write("My symbol: " + str)	My symbol: ⋽

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