Under what definition of division is (a/b)*b=a true for all values?
IIUC, codeflo is arguing that the division operation defined in the article isn't "actual division" because (a/b)*b=a isn't true for all values. But I can't think of a definition of division that satisfies that criteria.
The parallel in programming would be the contract : you provide a function that works on a given set of values. Or the type: the function would "crash" if you passed a value not of the type of its parameter, but it is admitted it won't be done.
(In the remaining I'm referring to 1/x instead of a/b to simplify things a bit)
Another way of saying it is that the function is undefined for 0. (Or on {0}). Then the property is true for all values (on which the function is defined, but saying it is redundant, the function can't be called outside its domain, it is an error to try to do this).
The domain is often left out / implicit, but it is always part of the definition of a function.
0 is not in the domain, so it's not to be considered at all when studying the function (except maybe when studying limits, but the function will still not be called with it).