Classification of zero polynomial

Question

Zero polynomial is a univariate or multivariate polynomial or this classification is not defined for it?

Answer 1

The symbol $0$ can signify many things. It could mean the natural number $0$, or the real number $0$, or the zero function $\Bbb R\to\Bbb R$, or the zero polynomial in the ring of complex polynomials in the three variables $x,y,z$. And many, many others.

Technically all these $0$'s are different. But their properties are so similar (even in the possible interactions between the algebraic structures mentioned above) that I don't know a single person who makes that difference explicit.

It does have some merit in specific problems and exercises. But then it's mostly because of how it helps the mental bookkeeping and not because of philosophical qualms with this abuse of notation.