TeXipedia

gneq

Represents a strict inequality indicating 'greater than and not equal to' in mathematical expressions.

Overview

Serves as a specialized relational operator commonly used in advanced mathematics and formal proofs where precise inequality relationships need to be specified.

  • Essential in set theory and analysis for expressing strict non-equality relationships
  • Often appears in mathematical logic and formal mathematical writing
  • Particularly useful when distinguishing between general inequality and specific non-equality cases
  • Provides a more formal and precise alternative to combining > with ≠

Examples

Comparing two non-equal expressions where one is strictly greater than the other.

x2+1⪈x2for all x∈Rx^2 + 1 \gneq x^2 \quad \text{for all } x \in \mathbb{R} 
x^2 + 1 \gneq x^2 \quad \text{for all } x \in \mathbb{R}

Showing a strict inequality between infinite series.

∑n=1∞1n⪈∑n=2∞1n\sum_{n=1}^{\infty} \frac{1}{n} \gneq \sum_{n=2}^{\infty} \frac{1}{n} 
\sum_{n=1}^{\infty} \frac{1}{n} \gneq \sum_{n=2}^{\infty} \frac{1}{n}

Demonstrating strict inequality between function values.

f(x+h)⪈f(x)+f′(x)hfor h>0f(x+h) \gneq f(x) + f'(x)h \quad \text{for } h > 0 
f(x+h) \gneq f(x) + f'(x)h \quad \text{for } h > 0