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gnsim

Represents a negated greater-than relation with a tilde, indicating 'not greater than and not similar to' in mathematical expressions.

Overview

Serves as a specialized comparison operator in advanced mathematical notation, particularly useful in abstract algebra, topology, and set theory where precise negation of both magnitude and similarity relationships is needed.

  • Common in formal mathematical proofs where strict relationships between elements or sets must be specified.
  • Particularly useful when working with partial orders and equivalence relations.
  • Often appears alongside other comparison operators in complex mathematical statements where multiple relationships need to be negated simultaneously.

Examples

Expressing that two functions are not asymptotically equivalent.

f(x)⋧g(x) as x→∞f(x) \gnsim g(x) \text{ as } x \to \infty 
f(x) \gnsim g(x) \text{ as } x \to \infty

Indicating non-similarity in statistical distributions.

X1⋧X2X_1 \gnsim X_2 
X_1 \gnsim X_2

Denoting that two algebraic structures are not generally similar.

G1⋧G2G_1 \gnsim G_2 
G_1 \gnsim G_2