I would agree with HoI's reply. Numbers, as mathematical expressions and statements in general, are independent of notation (be it symbols, numeral systems, or different human languages). The statement encapsulated by the statement in decimal numerals: 1+1=2 is still true in binary: 1+1=10.
You can define numbers starting with any base, but individual definitions are needed for each digit that are more basic than the notion of a set. It doesn't matter which number system you use because they all equivalent notations of the same thing.