> Reals form a group under multiplication. I think his point was that 0 has no inverse. So in the literal sense, the reals are not a group under multiplicatio

> Reals form a group under multiplication. I think his point was that 0 has no inverse. So in the literal sense, the reals are not a group under multiplication (although obviously, when somebody says "the reals are a group under multiplication", one usually interprets it as "R\{0} is a group under multiplication".) This is vaguely relevant to the issue at hand because we are doing 0 to the 0.