Vtyjkyuk

In the limits and continuity chapter in my textbook, the following definitions are given:

(1) For limit of f(x) as x tends to infinity:

We say that $ƒ(x)$ has the limit $L$ as $x$ approaches infinity and write $lim_xto infty f(x) = L$ if, for every number $epsilon > 0$ there exists a corresponding number $M>0$ such that for all $x>M, |f(x) - L| < epsilon$.

(2) For infinite limits:

We say that $ƒ(x)$ approaches infinity as $x$ approaches $x_0$, and write $lim_xto x_0 ƒ(x) = infty$, if for every number $B>0$ there exists a corresponding $delta > 0$ such that for all $x$,
$$0 < |x - x_0| < delta implies f(x) > B$$

What I don't understand is why the numbers M and B have to be greater than zero in the first and second definitions respectively. I think the definition would work without this added constraint, i.e. if M (and, similarly, B) is any real number.
So, I don't understand why this condition is present in the definitions.

Since I couldn't find any discussion on this topic anywhere on the net or in my book, I have asked this question.

What am I missing?