> Obviously zero is not 'approximately' equal to infinity as the previous author > might be claiming (??? I couldn't quite follow some of it). > > zero IS an approximation to 0.1, actually a first-order approximation, though I > suspect that isn't quite what the author had in mind. > > In fact (I write as someone with an Oxford maths degree), although the Natural > numbers (counting numbers 1, 2, 3, 4 etc) are perfectly adequate for > enumeration and addition, if one starts using subtraction and division then 0 > and infinity are required to turn the numbers into a field (or ring) with 2 > operators, otherwise there are too many complications (eg -1+1=1 and similar). > > Nothing can be taken for granted when counting the postive and negative > integers.
That's true, but where this all started requires an Oxford *physics* degree to understand, since we're really discussing Newton's somewhat useless *limits*.