# Computational Symbols

O ("big-oh", "capital O"); ASCII: `79`, Unicode: `U+004F`, HTML: `&#79;`
1. Big-Oh notation (computational complexity): `O(f(x))` denotes the asymptotic upper-bound on the runtime of function `f(x)`, typically expressed in terms of the size `n` of the input `x`. For example, if `x` contains `n` elements and the worst-case runtime of `f(x)` is linear in the size of `x`, then `O(f(x)) = n`. If the worst-case runtime of `f(x)` is quadratic in the size of `x`, then `O(f(x)) = n^2` (`n`-squared). [ref]
Ω ("omega", aka "weird O"); ASCII: `937`, Unicode: `U+03A9`, HTML: `&#937;`
1. Omega notation (computational complexity): `Ω(f(x))` denotes the asymptotic lower-bound on the runtime of function `f(x)`, typically expressed in terms of the size `n` of the input `x`. For example, if `x` contains `n` elements and the best-case runtime of `f(x)` is linear in the size of `x`, then `Ω(f(x)) = n`. [ref]
Θ ("theta", aka "O with line"); ASCII: `920`, Unicode: `U+0398`, HTML: `&#920;`
1. Theta notation (computational complexity): `Θ(f(x))` denotes a tight bound on the asymptotic runtime of function `f(x)`, typically expressed in terms of the size `n` of the input `x`. For example, if `x` contains `n` elements and the exact runtime (up to a constant factor) of `f(x)` is linear in the size of `x`, then `Θ(f(x)) = n`. [ref]