TeXipedia

lessgtr

Represents a mathematical relation indicating that one value is alternately less than and greater than another.

Overview

Commonly used in mathematical analysis and number theory to express oscillating comparisons between quantities or sequences.

  • Appears in discussions of alternating inequalities and sequence behavior.
  • Useful when describing comparative relationships that switch between less than and greater than.
  • Often encountered in advanced algebra and analysis when discussing convergence properties.
  • Provides a concise way to indicate non-monotonic relationships between mathematical expressions.

Examples

Comparing two variables that have a changing relationship over time.

x≶y as t→∞x \lessgtr y \text{ as } t \to \infty 
x \lessgtr y \text{ as } t \to \infty

Expressing uncertainty in the relationship between two economic indicators.

GDP growth≶inflation rate\text{GDP growth} \lessgtr \text{inflation rate} 
\text{GDP growth} \lessgtr \text{inflation rate}

Comparing sequences where relative magnitude varies with index.

an≶bn for n∈Na_n \lessgtr b_n \text{ for } n \in \mathbb{N} 
a_n \lessgtr b_n \text{ for } n \in \mathbb{N}