nmid

Indicates non-divisibility between numbers or a negated divides relationship in mathematical notation.

Overview

Serves as the negation of the divides symbol (|) in number theory and abstract algebra, commonly used to express that one number does not divide another evenly.

Essential in number theory proofs and algebraic statements
Frequently appears in discussions of divisibility properties
Used in mathematical logic and set theory to denote non-division relationships
Particularly useful when discussing prime numbers and factorization

Examples

Expressing that a number is not a divisor of another number.

3 \nmid 10

3 \nmid 10

Showing multiple non-divisibility relationships in number theory.

2 \nmid 15 \text{ and } 3 \nmid 16

2 \nmid 15 \text{ and } 3 \nmid 16

Demonstrating that a prime does not divide a product.

p \nmid ab \implies p \nmid a \text{ and } p \nmid b

p \nmid ab \implies p \nmid a \text{ and } p \nmid b