An English dictionary is not really going to tell you what mathematicians are doing. Like, its goal is to describe what the word “integer” means (in various contexts), it won’t tell you what the “integer series” is.
The gist I see is that it’s kind of ambiguous whether the whole number series includes negatives or not, and in higher math you won’t see the term without a strict definition. It’s much more likely you’d see “non-negative integers” or the like.