The Mathematical Symbol "Not True (⊭)"

The "Not True" Symbol (⊭): Denying Logical Truth

In the vast landscape of logical symbols, each serves a unique purpose, elegantly encapsulating intricate logical relationships. The ⊭ symbol, referred to as "Not True", is one such marker. Predominantly used in mathematical logic and formal proofs, it asserts that a particular statement is not a logical truth in the given structure. This article aims to shed light on the meaning, relevance, and application of ⊭.

Unveiling the ⊭ Symbol

While many may be familiar with the "models" symbol (⊨) that claims a statement is true in a particular model, ⊭ stands as its negation. It effectively says that a statement doesn't hold true, or a given model does not satisfy the statement.

Example 1: Invalid Propositions

If we have a logical system in which the proposition \( P \) doesn't hold true, we can represent this as: \( S ⊭ P \), where \( S \) is our system.

Example 2: Non-Satisfying Models

Consider a model \( M \) for a set of formulas. If \( M \) does not satisfy a particular formula \( F \), it can be articulated as: \( M ⊭ F \).

Realms of ⊭ Usage

The applications of ⊭ are rooted deeply in:

  • Mathematical Logic: To denote that certain axioms don't model a proposition.
  • Theoretical Computer Science: To indicate that an algorithm or structure doesn't satisfy a property or condition.
  • Formal Semantics: Demonstrating that a particular interpretation doesn't make a sentence true.

Its importance lies in its ability to indicate non-truth efficiently, making it crucial for maintaining clarity and precision in logical arguments and discussions.

To sum up, ⊭ is an integral notation in logic and related disciplines, enabling scholars and practitioners to succinctly convey the non-truth of statements. Its presence underscores the complexities and nuances of logical reasoning, making it an invaluable tool in the mathematical lexicon.

Mathematical symbol 'Not True'

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Codes for the ⊭ Symbol

The Symbol
Alt CodeAlt 8877
HTML Code⊭
HTML Entity⊭
CSS Code\22AD
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 8877. 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: &#8877;</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: "\22AD";}
<span>My symbol:</span>
My symbol: ⊭

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

HTML TextOutput
<b>My symbol: &#x22AD;</b>My symbol: ⊭
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x22AD 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+22AD. 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 22AD turns into ⊭. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u22AD. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u22AD"
document.write("My symbol: " + str)
My symbol: ⊭