Not Sign

ASCII Code: 172•Category: symbols

The not sign (¬) is a logical operator used in mathematics, computer science, and formal logic to represent negation, indicating the logical opposite or complement of a given statement or condition.

Technical Details

ASCII Code: 172
HTML Entity: ¬
Hexadecimal: 0xAC
Binary: 10101100
Octal: 254

Usage & Examples

Programming

char symbol = '¬'; // ASCII 172

HTML/Web

¬ or ¬

Common Uses

notlogicalnegationbooleanmathematics

How to Type This Character

Windows

Alt Code:

Hold Alt and type172 on numeric keypad

Character Map:

Search "Character Map" in Start menu

Mac

Character Viewer:

Press Ctrl +Cmd +Space

Copy & Paste:

Easiest method - copy from this page!

💡 Pro tip: The fastest way is to bookmark this page or copy the character from our ASCII library!

Related Characters

About the Not Sign

Logical Operations

Fundamental to propositional logic and Boolean algebra, the not sign transforms true statements to false and false statements to true. Essential for constructing complex logical expressions, proof systems, and mathematical reasoning in formal logic and set theory.

Computer Science

Critical in programming languages for Boolean operations, conditional statements, and logical expressions. While most languages use '!' or 'NOT' keywords, the ¬ symbol appears in academic computer science, formal specifications, and mathematical programming contexts.

Mathematical Logic

Standard notation in formal logic textbooks, mathematical proofs, and academic papers for expressing negation. Enables precise mathematical communication in fields like discrete mathematics, logic theory, and philosophical logic.

Circuit Design

Used in digital logic and circuit design to represent NOT gates and inverter circuits. Electronic engineers employ ¬ in logic diagrams, truth tables, and Boolean function specifications for digital system design.

History of the Not Sign

1800s

Symbolic Logic Development

Mathematicians like George Boole and Augustus De Morgan developed symbolic logic systems that required clear negation notation, leading to various symbols including the not sign for logical complement operations.

Early 1900s

Mathematical Standardization

Logic textbooks and mathematical publications began standardizing the ¬ symbol for negation alongside other logical operators, establishing consistent notation for formal mathematical reasoning.

1940s-1950s

Computer Science Integration

Early computer scientists and digital circuit designers adopted ¬ for representing logical NOT operations in theoretical work, Boolean algebra, and digital system specifications.

1960s

ASCII and Character Sets

Computer character encoding standards included the not sign to support mathematical and logical notation in digital documents, academic publishing, and technical communications.

Modern Era

Academic Continuation

Contemporary mathematics, computer science, and philosophy programs continue using ¬ in formal logic education, research papers, and theoretical work, maintaining its role in academic discourse.

Cultural Impact

The not sign enabled precise mathematical expression of logical negation, contributing to advances in computer science, artificial intelligence, and formal reasoning systems that underpin modern digital technology.

Usage Examples

Propositional Logic

Example

¬P (not P), ¬(A ∧ B) ≡ (¬A ∨ ¬B), ¬¬P ≡ P

Basic negation and De Morgan's laws in formal logic

Boolean Algebra

Example

¬A + A = 1, ¬A · A = 0, ¬(¬A) = A

Boolean complement operations and identities

Set Theory

Example

¬(x ∈ A) means x ∉ A, A ∩ ¬A = ∅

Set complement and membership negation

Digital Logic

Example

NOT gate: Y = ¬A, NAND gate: Y = ¬(A ∧ B)

Logic gate notation in circuit design and electronics