> George Greene <gree...@email.unc.edu> writes: > > Basically, any infinity of steps that has > > a last element will have an answer to this question. > > Any infinite sequence that does not have a last element > > needs to get its "answer" from some NON-standard convention.
On Nov 24, 2:30 pm, "Jesse F. Hughes" <je...@phiwumbda.org> wrote: > No, that's not enough. > > Suppose that the light begins "on", at each step, I toggle the state.
That was NOT the statement of the problem. The statement of the problem was >> you switch a light bulb on and off;
This is inviting people to map to real-world binary light-switches, NOT abstract unary togglers! If the light switch actually has positions MARKED on and off (here they are usually up and down), then this IS enough. But of course you are right in principle that if "toggling the state" AS OPPOSED to "turning on and off" is what is going on, then, yes, we are still confused.
> It seems that you agree that after omega-many steps, we do not know > whether the light is on or off. But if we do not know at omega > whether the light is on or off, then surely we do not know whether it > is on or off at omega + 1. > > Right?
Right, if the switch just toggles. But if the switch actually has on and off positions and you are just setting it to one, at every step, well, that's different. Oddly. I mean, it seems like it SHOULDN'T be different.
> To put it differently, you claim "any infinity of steps that has > a last element will have an answer to this question." w + 1 is an > "infinity of steps" with a last element, but if we have an answer at > w + 1, then we also have an answer at w.
Well, if you're toggling, yes. If you're turning on and off, then, well, it might still be possible to turn (e.g.) on, at w+1, even if you didn't know where you were at w.