"Frederick Williams" <firstname.lastname@example.org> wrote in message news:512CF70E.589D832E@btinternet.com... > Don Kuenz wrote: >> >> Joseph Nebus <nebusj-@-rpi-.edu> wrote: >> > >> > A couple recent posts on James Nicoll's LiveJournal --- >> > >> > http://james-nicoll.livejournal.com/4145868.html >> > http://james-nicoll.livejournal.com/4194844.html >> > >> > --- have left me aware that at least two Heinlein novels (_The Number >> > Of The Beast_ and _Time Enough For Love_) contain mentions dismissing >> > the Cantorian idea of there being different-size infinities, and that >> > at least one Christopher Anvil story in which a journey to hyperspace >> > reveals that the rationals and the integers *don't* have the same >> > cardinality. >> >> A question for the group, if you please. >> >> Let's say a Mobius strip goes to infinity "feedback style" (in layman's >> terms) while a line goes to two separate but equal infinities "linear >> style." How many different infinities does that make according to >> Cantor? One, two, or three? > > If you're interested in infinity, here is something that I posted > recently: > > A few years ago Zdislav V. Kovarik made a post listing a dozen or more > meaning of the word "infinity" as used in different branches of > mathematics. I'm hoping that he won't mind me reposting it: > > > There is a long list of "infinities (with no claim to exhaustiveness): > infinity of the one-point compactification of N, > infinity of the one-point compactification of R, > infinity of the two-point compactification of R, > infinity of the one-point compactification of C, > infinities of the projective extension of the plane, > infinity of Lebesgue-type integration theory, > infinities of the non-standard extension of R, > infinities of the theory of ordinal numbers, > infinities of the theory of cardinal numbers, > infinity adjoined to normed spaces, whose neighborhoods are > complements of relatively compact sets, > infinity adjoined to normed spaces, whose neighborhoods are > complements of bounded sets, > infinity around absolute G-delta non-compact metric spaces, > infinity in the theory of convex optimization, > etc.; > > each of these has a clear definition and a set of well-defined rules > for handling it.
In case you're maintaining a list, there's also "the point at infinity" that comes up with you're dealing with Elliptic Curve groups.