A doubt regarding the acceptance of $\epsilon$ by an automaton testing divisibility of numbers As we know, $\epsilon$ is the empty string, with length 0. It is not part of any any alphabet by default, unless specifically defined so. However, it is a string over any alphabet.

For example, Given that I need to design a Deterministic or Nondeterministic finite state automaton (without $\epsilon$ transitions) that accepts decimal numbers that are say, divisible by 2, would I have to account for the empty string as an input word as well? If so, how does divisibility work for null input?
It is rather standard to assume that 0 represents zero (and is divisible by two). Also it is usually assumed that decimal numbers do not start with 0.

I once presented a finite state automaton without these assumptions, where I took  $\varepsilon$ as a representation for zero, and likewise 0000, and my students protested.