Triple Vertical Bar Right Turnstile

The Mathematical Symbol "Triple Vertical Bar Right Turnstile (⊪)"

The ⊪ Symbol in Mathematics: Triple Vertical Bar Right Turnstile

The ⊪ symbol, also known as the "Triple Vertical Bar Right Turnstile", is a special logical notation. Though not as common as some other mathematical symbols, it holds a significant place in certain formal logic and proof systems. This article will clarify its meaning and provide a couple of illustrative examples.

Usage

The ⊪ sign is commonly used in formal logic to show a stronger form of logical consequence or derivability. When a statement or set of statements leads to a particular conclusion in a given logical system, the turnstile is used to indicate this relationship. The triple bar adds emphasis, usually indicating a stronger or more specific form of consequence within the system.

Examples

• Example 1: Formal Systems:
  In a formal system, if a set of axioms \( A \) leads to a theorem \( T \) under a specific set of rules, one might express this relationship as \( A ⊪ T \), especially if the derivation is especially strong or robust.
• Example 2: Model Theory:
  In model theory, the triple vertical bar right turnstile might be used to show that a particular structure or model satisfies a given set of sentences, especially when the satisfaction is considered in a stronger sense or under more stringent conditions.

In summary, the ⊪ symbol plays a crucial role in formal logic and related fields, enabling mathematicians and logicians to express specific forms of logical consequence or derivability. It exemplifies the depth and variety of notations that cater to the nuances of mathematical and logical relationships.

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Codes for the ⊪ Symbol

The Symbol	⊪	copy
Alt Code	Alt 8874	copy
HTML Code	⊪	copy
HTML Entity	⊪	copy
CSS Code	\22AA	copy
Hex Code	⊪	copy
Unicode	U+22AA	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 8874. 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: &#8874;</b>	My symbol: ⊪

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

HTML Text	Output
<b>My symbol: &Vvdash;</b>	My symbol: ⊪

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

CSS and HTML Text	Output
<style> span:after { content: "\22AA";} </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: &#x22AA;</b>	My symbol: ⊪

On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x22AA 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+22AA. 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
22AA [Hold down Alt] [Press x]	⊪ (The 22AA turns into ⊪. Note that you can omit any leading zeros.)

In JavaScript, the syntax is \uXXXX. So, our example would be \u22AA. (Note that the format is 4 hexadecimal characters.)

JavaScript Text	Output
let str = "\u22AA" document.write("My symbol: " + str)	My symbol: ⊪

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