TeXipedia

leqq

Represents a less-than-or-equal-to relationship with an additional equals sign for emphasis in mathematical expressions.

Overview

Serves as a specialized comparison operator in advanced mathematical notation, particularly useful in formal proofs and precise mathematical writing.

  • Common in abstract algebra and analysis for expressing refined inequalities
  • Often used when emphasizing the equality case in less-than-or-equal relationships
  • Appears in theoretical computer science and mathematical logic for formal specifications
  • Helpful in contexts where distinguishing between different types of inequalities is important

Examples

Expressing a less-than-or-equal relationship with a double underline in a mathematical inequality.

x≦y  ⟹  f(x)≦f(y)x \leqq y \implies f(x) \leqq f(y) 
x \leqq y \implies f(x) \leqq f(y)

Showing nested inequalities with mixed comparison operators.

0≦x≤1≦y<∞0 \leqq x \leq 1 \leqq y < \infty 
0 \leqq x \leq 1 \leqq y < \infty

Defining a bounded sequence in analysis.

−M≦an≦M for all n∈N-M \leqq a_n \leqq M \text{ for all } n \in \mathbb{N} 
-M \leqq a_n \leqq M \text{ for all } n \in \mathbb{N}