DavidW wrote: > Tom P wrote: >> On 03/10/2012 09:23 PM, Harrison Hill wrote: >>> Whoever, whomever or whomsoever they are, they need "who". >> True. And there are indeed infinities that are larger than others, in >> fact infinitely many. > > No, there are not. > >> The set of real numbers is larger then the set >> of integers, for example. > > No. You start giving me real numbers and for each one I'll give you an integer. > We can keep doing that for as long as you like and I will never run out of > integers. Now you'll probably say that you didn't really mean "larger" after all > and want to bring up bijections and cardinality and such like. Save it.
I was wondering when this would happen. The question of "who" vs "whom" can be settled in a couple of sentences; but introduce a question of mathematical philosophy into alt.usage.english and the thread can go on forever.
I'm in the Cantor camp myself. If you can't conceive of uncountable infinities then measure theory has to be re-done from the bottom up, and things like integration become conceptually harder. Not to mention concepts like continuity, limits, and so on. Yes, I'll concede that you can build a mathematics on treating everything as countable, but as a believer in Ockham's razor I prefer not to multiply complexity like that.
Having said that, I'll try to shut up, precisely because of that thread-goes-on-forever phenomenon. If you start crowding out things like sheep and food then it's not really an English usage group.