TeXipedia

succapprox

Denotes a succeeds or approximately follows relationship between mathematical expressions, combining the concepts of succession and approximation.

Overview

Serves as a specialized mathematical relation symbol that combines the meaning of succession with approximation, particularly useful in advanced mathematics and theoretical computer science.

  • Common in order theory and abstract algebra when describing sequences or ordered sets
  • Used to indicate that one element follows another while being approximately equal
  • Appears in formal proofs and mathematical analysis where precise ordering relationships need to be specified with some degree of approximation
  • Helpful in describing asymptotic behavior and limit relationships

Examples

Comparing sequences in analysis, showing one sequence succeeds and is approximately equal to another.

an⪸bn as n→∞a_n \succapprox b_n \text{ as } n \to \infty 
a_n \succapprox b_n \text{ as } n \to \infty

Expressing a relationship between functions where one dominates and approximates another.

f(x)⪸g(x) for x>Mf(x) \succapprox g(x) \text{ for } x > M 
f(x) \succapprox g(x) \text{ for } x > M

Describing asymptotic behavior in complexity analysis.

T(n)⪸nlog⁡nT(n) \succapprox n\log n 
T(n) \succapprox n\log n