Big O Notation is formally defined as:
Let $f(n)$ and $g(n)$ be function from positive integers to positive reals. We say $f = \theta(g)$ (which means that "$f$ grows no faster than $g$*) if there is a constant $c>0$ such that $f(n) ≤ c ⋅ g(n)$.
Using this definition how is:
- $n^2 + n$ simplified to $n^2$
- $n + 20$ simplified to $n$
I don't see a $c$ constant that defines their relationship. How do the above examples work?