That depends on which concept of "number" and which foundation you would accept as a basis for doing arithmetic. I would expect any useful system of arithmetic

That depends on which concept of "number" and which foundation you would accept as a basis for doing arithmetic. I would expect any useful system of arithmetic, offering addition and subtraction, to contain some concept of "nothing". Because if a is something that might be subtracted from anything else including itself, we have the result that a - a is something we should be able to talk about, namely nothing. If you accept a sufficiently strong set theory as a foundation of mathematics, for example the Zermelo Fraenkel set theory including the axiom of choice (ZFC), it is possible to use the finite ordinal numbers - which are actually sets - as the natural numbers. From the ZFC axioms we have the existence of the empty set, often denoted by a pair of empty brackets {}. We can then define numbers by using the empty set: 0 := {} 1 := {0} = {{}} 2 := {0,1} = {{},{{}}} ... and so on. By this definition zero is a number. On the other hand, by defining numbers on the basis of set theory we seem to accept that numbers are sets. Some people will have very different opinions about this matter.