The Mathematical Symbol "Negated Double Vertical Bar Double Right Turnstile (⊯)"

Unpacking the "Negated Double Vertical Bar Double Right Turnstile" Symbol (⊯)

In mathematical logic and related disciplines, the ⊯ symbol, known as the "Negated Double Vertical Bar Double Right Turnstile", plays a crucial role.

Meaning of ⊯

The ⊯ symbol signifies a specific logical relationship that negates the assertion of "models" or "forces". In essence, it states that a certain logical formula does not hold in a given structure or context. It is the negation of the ⊫ symbol, which asserts that a formula is true or is forced by another formula or set of formulas.

Example 1: Model Theory

Let's assume \( M \) is a structure and \( \phi \) is a formula. If \( M \) does not model \( \phi \), we can express it as: \[ M ⊯ \phi \]

Example 2: Proof Theory

If a set of formulas \( \Gamma \) does not force a formula \( \psi \) to be true, we can write: \[ \Gamma ⊯ \psi \]

Applications of ⊯

The ⊯ notation is pivotal in various mathematical realms, including:

  • Model Theory: To indicate that a specific structure doesn't satisfy a given formula.
  • Proof Theory: To signify that a certain formula isn't derivable or provable from a set of other formulas.

In summary, the ⊯ symbol is an invaluable tool for expressing negations in logical relationships, particularly in contexts where the validity or provability of formulas is under scrutiny. Understanding its significance is instrumental in fields such as mathematical logic and computer science.

Mathematical symbol 'Negated Double Vertical Bar Double Right Turnstile'

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Codes for the ⊯ Symbol

The Symbol
Alt CodeAlt 8879
HTML Code⊯
HTML Entity⊯
CSS Code\22AF
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 8879. 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: &#8879;</b>My symbol: ⊯

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

HTML TextOutput
<b>My symbol: &nVDash;</b>My symbol: ⊯

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

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

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

HTML TextOutput
<b>My symbol: &#x22AF;</b>My symbol: ⊯
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x22AF 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+22AF. 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 22AF turns into ⊯. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u22AF. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u22AF"
document.write("My symbol: " + str)
My symbol: ⊯