asymp
Denotes asymptotic equivalence between mathematical expressions, indicating they approach the same value or behavior in a limit.
Overview
Essential in mathematical analysis and computer science for comparing the growth rates or limiting behavior of functions.
- Commonly used in complexity theory to describe algorithmic efficiency.
- Appears frequently in asymptotic analysis of sequences and series.
- Important in approximation theory when describing how closely functions match as variables approach infinity.
- Distinguished from similar relations like \sim by specifically indicating that the ratio of two quantities approaches 1.
Examples
Comparing the asymptotic behavior of two functions.
f(n) \asymp n^2Expressing asymptotic equivalence in computational complexity.
T(n) \asymp \log nShowing asymptotic relationship between sequences.
a_n \asymp \frac{1}{n}