2 ms·
You have to add extra "except when"s to every theorem involving division. E.g.: (a+b)/c = a/c + b/c (in particular, for C != 1, as the author claimed it would
by j2kun 8y ago
You have to add extra "except when"s to every theorem involving division. E.g.:
(a+b)/c = a/c + b/c
(in particular, for C != 1, as the author claimed it would work not just for 0 for for any real number)
Now to say this is true you have to say "unless c = 0", whereas before that was automatic from the definition of division.
- hyperpape 8y agoThe same theorem forall c != 0, (a+b)/c = a/c + b/c is true before and after. It may be helpful to observe that while using the same symbol '/' in both cases is confusing, mathematical theorems are not about symbols, but about particular mathematical objects. The old theorem is about the division relation defined for real numbers != 0, the new one is a relation defined for all real numbers, that just happens to coincide.
- j2kun 8y agoThat is exactly my point. Now you have to disambiguate a poorly-chosen symbol. The theorem doesn't need the stipulation that c != 0 since you have already excluded c from the domain.