TeXipedia

succsim

Represents a mathematical relation indicating 'succeeds or is similar to', combining the concepts of succession and similarity.

Overview

Serves as a specialized comparison operator in mathematical notation, particularly useful in order theory and abstract algebra.

  • Common in formal mathematical proofs and theoretical computer science.
  • Used when describing sequences, orderings, or relationships that exhibit both successive and similar properties.
  • Appears alongside related operators like \prec and \succ in formal mathematical writing.
  • Particularly valuable in contexts where standard inequality symbols are insufficient to capture the precise mathematical relationship.

Examples

Comparing sequences where one grows at least as fast as another.

an≿bn as n→∞a_n \succsim b_n \text{ as } n \to \infty 
a_n \succsim b_n \text{ as } n \to \infty

Expressing asymptotic dominance in computational complexity.

f(n)≿g(n)f(n) \succsim g(n) 
f(n) \succsim g(n)

Comparing convergence rates of numerical methods.

∥ek+1∥≿∥ek∥2\|e_{k+1}\| \succsim \|e_k\|^2 
\|e_{k+1}\| \succsim \|e_k\|^2