TeXipedia

nsim

Denotes a relationship that is explicitly not similar between mathematical expressions or geometric objects.

Overview

Serves as a negation of the similarity relationship in mathematical notation, particularly useful in geometry, algebra, and set theory.

  • Common in proofs and mathematical arguments where dissimilarity needs to be explicitly stated
  • Used when comparing geometric shapes, algebraic expressions, or mathematical structures
  • Frequently appears alongside other comparison symbols in formal mathematical writing
  • Essential in contexts where precise mathematical relationships need to be clearly distinguished

Examples

Expressing that two distributions are not similar.

P(X)P(Y)P(X) \nsim P(Y)
P(X) \nsim P(Y)

Indicating non-similar triangles in geometry.

ABCDEF\triangle ABC \nsim \triangle DEF
\triangle ABC \nsim \triangle DEF

Showing that two functions do not have similar behavior.

f(x)g(x) as xf(x) \nsim g(x) \text{ as } x \to \infty
f(x) \nsim g(x) \text{ as } x \to \infty