TeXipedia

precsim

Represents a mathematical relation combining precedence and similarity, indicating one element precedes and is approximately equal to another.

Overview

Serves as a specialized mathematical operator commonly found in order theory and analysis where approximate precedence relationships need to be expressed precisely.

  • Often used in mathematical proofs and formal mathematical writing where both ordering and approximation need to be conveyed simultaneously.
  • Appears in contexts involving asymptotic analysis and sequence comparisons.
  • Particularly useful in papers and documents discussing ordered structures with approximate relationships.

Examples

Comparing asymptotic behavior of functions where one grows more slowly.

f(n)g(n) as nf(n) \precsim g(n) \text{ as } n \to \infty
f(n) \precsim g(n) \text{ as } n \to \infty

Expressing that one sequence is asymptotically dominated by another.

{an}{bn}\{a_n\} \precsim \{b_n\}
\{a_n\} \precsim \{b_n\}

Comparing computational complexity bounds.

T1(n)T2(n)T_1(n) \precsim T_2(n)
T_1(n) \precsim T_2(n)