TeXipedia

lvertneqq

Denotes a strict inequality with a vertical line on the left side, commonly used in mathematical expressions to show distinct non-equality.

Overview

Serves as a specialized relational operator in advanced mathematics, particularly useful in set theory, analysis, and abstract algebra where precise inequality notation is essential.

  • Often employed when standard inequality symbols are insufficient to convey specific mathematical relationships
  • Frequently appears in formal mathematical proofs and academic papers
  • Particularly useful in contexts where left-sided vertical inequalities need to be distinguished from regular inequalities
  • Part of the extended AMS symbol collection for enhanced mathematical notation

Examples

Expressing that a vector's magnitude is strictly not equal to a scalar value.

∥x∥≨r\|x\| \lvertneqq r 
\|x\| \lvertneqq r

Showing that the absolute value of a complex number is strictly not equal to another.

∣z1∣≨∣z2∣|z_1| \lvertneqq |z_2| 
|z_1| \lvertneqq |z_2|

Indicating that the norm of a function is strictly not equal in a functional analysis context.

∥f∥≨M\|f\| \lvertneqq M 
\|f\| \lvertneqq M