2
$\begingroup$

This is from Discrete Mathematics and its Applications enter image description here

Shouldn't the if in that definition be an if and only if?
Say we know that $n^2$ is in O($n^2$). Then from one side of the if and only if, we know that there are constants c and $n_0$, in this case 1 and 0, such that $n^2$ <= 1* $n^2$ for all n>= 0?
But if we know that there are c and $n_0$, in this case 1 and 0, such that $n^2$ <= 1* $n^2$ for all n>= 0, can't we say that $n^2$ is in O($n^2$) from the other side of the if and if only if?

The book does use if and only if. Here is an example of it enter image description here

Would it be more appropriate for the big oh definition to include if and only if as well?

$\endgroup$