TeXipedia

precapprox

Represents a mathematical relation combining 'precedes' and 'approximately equal to' in a single symbol.

Overview

Serves as a specialized relational operator in mathematical notation, particularly useful in analysis and set theory where ordering and approximation need to be expressed simultaneously.

  • Common in sequences and series analysis where one term precedes and approximates another
  • Used in numerical mathematics when describing convergence with ordering relationships
  • Helpful in expressing asymptotic behavior where order relations combine with approximate equality

Examples

Comparing asymptotic behavior of functions where one precedes and is approximately equal to another.

f(n)⪷g(n)as n→∞f(n) \precapprox g(n) \quad \text{as } n \to \infty 
f(n) \precapprox g(n) \quad \text{as } n \to \infty

Expressing a relationship between sequences where one sequence precedes and approximates another.

{an}⪷{bn}\{a_n\} \precapprox \{b_n\} 
\{a_n\} \precapprox \{b_n\}

Comparing numerical values with both precedence and approximation in mathematical analysis.

3.14⪷π3.14 \precapprox \pi 
3.14 \precapprox \pi