## 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 | ⋽ | |

Alt Code | Alt 8957 | |

HTML Code | ⋽ | |

HTML Entity | ⋽ | |

CSS Code | \22FD | |

Hex Code | ⋽ | |

Unicode | U+22FD |

## 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: ⋽</b> | My symbol: ⋽ |

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

HTML Text | Output |
---|---|

<b>My symbol: ⋽</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: ⋽</b> | My symbol: ⋽ |

**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.) |

JavaScript Text | Output |
---|---|

let str = "\u22FD" 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.