Order Symbols

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There are two kinds of Order Symbols, one is the “small oh”, and another is the “big Oh”.

The small oh

Let $\{c_n\}$ and $\{a_n\}$ be sequence of real numbers, then

• $c_n\to o(1)$ is same as $c_n\to 0$ as $n\to \infty$.
• $c_n=o(a_n)$ means that ${\lim }_{n\to \infty }\frac{c_n}{a_n}=0$.

Intuitively, $c_n$ goes to zero faster than $a_n$.

The motivation of this notation is that, suppose $w_n=o(n)$, it means that $w$ grows no faster than $n$, for example.

The big Oh