I'm reading The Algorithm Design Manual and this is one of the excersizes:
Prove or disprove the following statement:
$\Theta(n^2 ) = \Theta(n^2 + 1)$
I think this is untrue because the right side of the equation claims to have a multiple $c$ such that it is smaller than all the multiples of $n^2$, which is untrue. But since the book doesn't have answers and I'm not really sure about this question I had to ask.
Thanks a lot :)