By some definitions, maybe. However, definitions that exclude it probably do so for a specific reason. It's more a fluke of categorization than a real world distinction. Those distinctions might be critical to certain logic systems, but even most people who use that definition recognize reality.

Zero is a number in more cases than it isn't. It is a symbol that represents a value. Just like infinity, it doesn't matter if 0 doesn't exist in physical reality. It's still a useful value in most cases.

Who told you that nonsense?

0 ∈ ℝ