Peter Percival writes: > Dan Christensen wrote: > > On Wednesday, November 13, 2013 5:22:21 PM UTC-5, Bart Goddard wrote: > >> > >> You should be able to dope this out, because the exact > >> same reasoning you're using, could be used to assert, > >> equally validly, that 2^2 should be left undefined. > > > > Wrong again, Barty. > > Why? Why not say > > ALL(a):ALL(b):ALL(c):[a e n & b e n & c e n => > [~a=2 => a^b * a^c => a^(b+c)]] > > Above you arbitrarily exclude a=0, why not exclude a=2 instead?
Dan starts from the fact that lots of people have long insisted that 0^0 must not be defined. It's been for no reason or for bogus reasons, but it's been and still is. Dan's got that right.
Powers like 2^2 don't have such history. I think that's the only difference.
That's not a formal reason, so why shouldn't 2^2 be undefined? It could be so why shouldn't it? When convenience is not a reason and formal simplicity is not a reason, what is?