Talk:Discrete Mathematics/Number representations

More generally, a number representation could be considered a number $$b$$ and a set of numbers $$D$$ known as "digits" (of which one is zero). Representation of other numbers in terms of an infinite sequence of digits (almost all of which are zero) then follows as before, i.e., $$\sum_{j=-\infty}^M d_j b^j,\, d_j\in D$$. Obviously, depending on $$b$$ and $$D$$, some numbers may be unrepresentable, or there may be numbers which have multiple representations (one or the other is unavoidable once you allow a continuum e.g. the Reals). I merely note this for discussion, because without conversion between $$b=10,\, D=\{0,1,2,3,4,5,6,7,8,9\}$$ and something like $$b=i-1,\, D=\{0,1\}$$ or $$b=-2,\, D=\{0, 1, \frac{-1\pm i\sqrt{3}}{2}\}$$ the information would go nowhere.