Big-Oh Notation: $a_k = O(b_k)$ if $\exist M \geq 0, \exist 1\leq k < \infty, \forall k \geq K:$

$$ a_k \leq M b_k $$

→ If $a_k = O(b_k)$ and $b_k = O(a_k)$, we say $a_k = \Theta(b_k)$ (Big-Theta Notation).

Little-Oh Notation: $a_k = o(b_k) \iff \lim_{k \rightarrow \infty} \frac{a_k}{b_k}=0$. This means that $b_k$ is an upper bound on $a_k$ that is not tight, hence why the limit approaches zero.

<aside> 💡 Every Little-Oh case is a Big-Oh case but not vice-versa. Both specify that $b$ is an upper-bound of $a$, but Little-Oh requires this upper bound to not be tight.

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