TeXipedia

leqslant

Represents a less-than-or-equal-to relationship with a slanted line beneath the symbol, providing a stylistic alternative to the standard notation.

Overview

Commonly used in mathematical expressions and proofs where precise inequality relationships need to be shown with enhanced visual clarity. The slanted variant offers improved readability, especially in complex mathematical formulas.

  • Popular in advanced mathematics and theoretical computer science
  • Often preferred in formal mathematical writing for its aesthetic appeal
  • Particularly useful in expressions involving multiple inequalities or mathematical optimization problems
  • Frequently appears in academic papers and textbooks focusing on analysis, algebra, and set theory

Examples

Expressing a less-than-or-equal relationship with a slanted symbol in an inequality.

x⩽y⩽zx \leqslant y \leqslant z 
x \leqslant y \leqslant z

Defining a set using set-builder notation with a slanted less-than-or-equal condition.

S={x∈R:−1⩽x⩽1}S = \{x \in \mathbb{R} : -1 \leqslant x \leqslant 1\} 
S = \{x \in \mathbb{R} : -1 \leqslant x \leqslant 1\}

Showing convergence conditions in a mathematical limit.

lim⁡x→0f(x)=L when ∣x−a∣⩽δ\lim_{x \to 0} f(x) = L \text{ when } |x - a| \leqslant \delta 
\lim_{x \to 0} f(x) = L \text{ when } |x - a| \leqslant \delta