The Mathematical Symbol "Not Sign (¬)"

The "Not Sign" Symbol (¬): Expressing Negation

In the diverse realm of mathematical notation, the ¬ symbol, commonly referred to as the "Not Sign," stands out as a straightforward indicator of negation or denial. It's a pivotal tool for expressing logical operations, particularly in the fields of mathematics, logic, and computer science. This article delves into its meaning, history, and applications.

Interpreting the ¬ Symbol

The primary function of the ¬ symbol is to represent negation or logical complement. In simple terms, when placed before a statement, it signifies the opposite of that statement.

Example 1: Logical Operations

If \( P \) is a proposition such as "It is raining," then ¬P would represent "It is not raining."

Example 2: Set Theory

Let \( A \) be a set in the universal set \( U \). The complement of \( A \), represented as ¬A, includes all elements in \( U \) that are not in \( A \).

Tracing the Origins

The ¬ symbol has its roots in classical logic. George Boole, in the 19th century, popularized its use in his revolutionary "Boolean algebra," which later became the foundational stone for digital logic and modern computing.

Areas of ¬ Application

The use of the ¬ symbol spans several disciplines:

  • Logic: To represent the negation of a proposition.
  • Set Theory: Denoting the complement of a set.
  • Computer Science: In binary operations, where ¬ transforms a 0 to 1 and vice versa.
  • Mathematics: To indicate the inverse of certain operations or conditions.

Though simple in design, the ¬ symbol is crucial for clarifying statements, conditions, and operations, ensuring that they are articulated with precision.

In summary, the ¬ symbol has firmly cemented its place in various disciplines, playing a critical role in depicting negation. Its universality and timeless relevance underscore its importance in academic, research, and practical applications.

Mathematical symbol 'Not Sign'

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Codes for the ¬ Symbol

The Symbol¬
Alt CodeAlt 172
HTML Code¬
HTML Entity¬
CSS Code\00AC
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 172. 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: &#172;</b>My symbol: ¬

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

HTML TextOutput
<b>My symbol: &not;</b>My symbol: ¬

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

CSS and HTML TextOutput
span:after {
content: "\00AC";}
<span>My symbol:</span>
My symbol: ¬

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

HTML TextOutput
<b>My symbol: &#x00AC;</b>My symbol: ¬
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x00AC 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+00AC. 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 00AC turns into ¬. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u00AC. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u00AC"
document.write("My symbol: " + str)
My symbol: ¬