TeXipedia

ngeqq

Represents a negated double-line greater-than-or-equal-to relationship between mathematical expressions.

Overview

Serves as a specialized relational operator in mathematical proofs and formal logic where strict inequality needs to be emphasized with double lines.

  • Common in advanced mathematics and theoretical computer science for expressing non-relationships.
  • Used when standard inequality symbols are insufficient to convey precise mathematical meaning.
  • Particularly useful in set theory, abstract algebra, and formal mathematical reasoning where detailed relationship distinctions are crucial.
  • Often appears alongside other specialized comparison operators in complex mathematical statements.

Examples

Expressing that one sequence is not greater than or equal to another sequence in the sense of pointwise comparison.

{an}≱{bn}\{a_n\} \ngeqq \{b_n\} 
\{a_n\} \ngeqq \{b_n\}

Showing a counterexample to a statement about real numbers.

x≱y  ⟹  f(x)<f(y)x \ngeqq y \implies f(x) < f(y) 
x \ngeqq y \implies f(x) < f(y)

Defining a strict ordering relation in a mathematical structure.

∀x,y∈S:x≱y  ⟺  x<y\forall x,y \in S: x \ngeqq y \iff x < y 
\forall x,y \in S: x \ngeqq y \iff x < y