On Mar 13, 12:28 am, "DavidW" <n...@email.provided> wrote: > quasi wrote: > > DavidW wrote: > >> quasi wrote: > >>> DavidW wrote: > > >>> It surely reduces the range of math you can do, but if that > >>> doesn't bother you, no problem. It's when you claim to have > >>> _proved_ that infinite sets don't exist, when in fact, your > >>> argument doesn't even come close to what anyone (respected > >>> finitists included) would accept as a rigorous proof -- > >>> that's when you get called a crank. > > >> It's pretty basic. You claim to have a "set" of natural numbers. > >> That normally means a container, > > > Sure, a set is a kind of container -- a conceptual container. > > >> but you cannot contain an infinite number of items. > > > You keep saying that, but how do you prove that your above > > claim holds in _our_ system. > > > In our system: > > Does your system have a point? I thought mathematics was about finding truths in > numbers.
**** Oh, dear! Did you get this one wrong or what! Hopefully by now you've already fixed your thoughts...****
Or have you just invented an arbitrary formal system to have fun with, > like a game of chess?
*** Exactly so. Only now have you realized this? Well, this is what happens when cranky brats stubbornly try to mess with things way over their level.
Mathematics in general, and set theory in particular, is precisely that: arbitrary (here we could discuss a while what this means in mathematics...but we won't, in fact) formal systems to have fun with. Like the game? Accept the rules and play along. Like the game but not the rules? Try to make up your own rules and if they're sound and interesting perhaps somebody else will join and play. Don't like the game? Back off and let intelligent people who like it play.