TeXipedia

ngeq

Represents the 'not greater than or equal to' relation, indicating that one value is neither greater than nor equal to another.

Overview

Essential for expressing strict inequalities and negative comparisons in mathematical proofs and formal logic statements.

  • Common in set theory and analysis when proving value relationships
  • Used to negate greater-than-or-equal-to statements in mathematical arguments
  • Particularly useful in advanced algebra and real analysis when establishing bounds
  • Often appears alongside other inequality symbols in complex mathematical expressions

Examples

Expressing that a sequence does not converge to a limit.

an≱L as n→∞a_n \ngeq L \text{ as } n \to \infty 
a_n \ngeq L \text{ as } n \to \infty

Stating an inequality constraint in optimization.

f(x)≱M for some x∈Xf(x) \ngeq M \text{ for some } x \in X 
f(x) \ngeq M \text{ for some } x \in X

Comparing sets by cardinality.

∣A∣≱∣B∣|A| \ngeq |B| 
|A| \ngeq |B|