In practical terms, that _does_ have an impact, because people might use those shortcuts without realising the system they’re operating under doesn’t allow it.
But you picked the wrong quote to make that point under.
If a==b and N≠0, then x==y
EDIT: Formatting
"Given an x, y, and N such that x/N == y/N, it is true that x == y".
There is no need to say N != 0 under the ordinary definition of division.
Many languages handle this in a practical way by creating a special value "undefined", "NaN", or others that has special properties. But let's be clear that "0" is a normal number in the real number space, as so expectations about properties of real numbers are not going to hold up.
Sure, and both are bad.
> To avoid this just don't do 1 / 0 in your program.
If you're going to avoid doing it, better to have it throw an exception if you do it by accident.
I didn't like the blogpost, because it's smug, and doesn't even mention this obvious objection.
a=x/N
b=y/N
If a==b, then x==y
No longer true, with this change. Essentially a variety of mathematical properties of numbers in the Real space don't hold when you allow division by 0.