I would assume the answer to my question is yes, but I want to make sure because my book uses both terminologies.  Please also indicate where zero falls into the mix.

UPDATE:

Here is an excerpt from my book:


  The definition of $\Theta(g(n))$ requires
  that every member $f(n) \in \Theta(g(n))$ be
  asymptotically non-negative, that is,
  that $f(n)$ be non-negative whenever n
  is sufficiently large. (An
  asymptotically positive function is
  one that is positive for all
  sufficiently large $n$.)


The real numbers can be partitioned into the positive real numbers, the negative real numbers, and zero.  A real number is one and only one of those three possibilities.  This is called "trichotomy."  Non-negative (or, correspondingly, non-positive) means not negative (not positive), so zero or positive (zero or negative).

That is, non-negative includes zero whereas positive does not.

Edit for clarity:

Non-negative means zero or positive.

Non-positive means zero or negative.

That is, non-negative includes zero whereas positive does not and vice versa.
