The Definition of Points
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From: Lester Zick on 31 Mar 2007 15:24 On 31 Mar 2007 07:07:38 -0700, "Brian Chandler" <imaginatorium(a)despammed.com> wrote: > >Tony Orlow wrote: >> stephen(a)nomail.com wrote: >> > In sci.math Virgil <virgil(a)comcast.net> wrote: >> >> In article <460d4813(a)news2.lightlink.com>, >> >> Tony Orlow <tony(a)lightlink.com> wrote: >> > >> > >> >>> An actually infinite sequence is one where there exist two elements, one >> >>> of which is an infinite number of elements beyond the other. >> >> >> >> Not in any standard mathematics. >> > >> > It is not even true in Tony's mathematics, at least it was not true >> > the last time he brought it up. According to this >> > definition {1, 2, 3, ... } is not actually infinite, but >> > {1, 2, 3, ..., w} is actually infinite. However, the last time this >> > was pointed out, Tony claimed that {1, 2, 3, ..., w} was not >> > actually infinite. >> > >> > Stephen >> >> No, adding one extra element to a countable set doesn't make it >> uncountable. If all other elements in the sequence are a finite number >> of steps from the start, and w occurs directly after those, then it is >> one step beyond *some step* which is finite, and so is at a finite step. > >Perhaps you might care, Tony, to list some properties of this "some >step" you have referred to above? I tell you what, I'll give you a >start - let's call this 'step' (actually this is the wrong word, since >step is normally the gap between two adjacent elements**, so let's >call this element) Q. > >** I'm sure you understand that being described as more logically >coherent (orwhateveritwas) than Lester Zick is rather like being >called more caring than Jack the Ripper, Or like arguing virtue between mathematikers and whores. > but I take the sentiment to >mean that you will probably agree with this nitpick about 'step' >terminology. > >So: > >Q has the property of being the last element in an endless sequence >Q has the property of nonexistence, actually > >Now it's your turn. > > > >> Try (...000, ..001, ...010, ......, ...101, ...110, ...111) > >Why? What is it, anyway? > >Brian Chandler >http://imaginatorium.org ~v~~
From: Virgil on 31 Mar 2007 15:26 In article <460e8432(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > stephen(a)nomail.com wrote: > > So you think there are only a finite number of elements between 1 and > > w? What is that finite number? 100? 100000? 100000000000000000? > > 98042934810235712394872394712349123749123471923479? Which one? > > > > Aleph_0, which is provably a member of the set, if it's the size of the > set. Of which set is TO claiming aleph_0 is "provably a member"? If it is the set of naturals, TO has not proved it and others have disproved it, so this is one of the occasions on which TO is wrong!. > > As I said, even you do not accept your own definition of "actually > > infinite". > > > > Stephen > > > > If you paid attention, the apparent contradiction would evaporate. The > number of elements up to and including any finite element of N is > finite, and equal to that element in magnitude. If the number is n, then > there's an nth, and its value is n. As Ross like to say, NeN. We are not > alone. :D Anything Ross says should be taken with a grain of salt the size of the Empire State Building. In particular, what set theory is Ross claiming allows any set to be a member of itself?
From: Lester Zick on 31 Mar 2007 15:28 On 31 Mar 2007 10:02:17 -0700, "Brian Chandler" <imaginatorium(a)despammed.com> wrote: >Tony Orlow wrote: >> Brian Chandler wrote: >> > Tony Orlow wrote: >> >> Hi Imaginatorium - > >That's not my name - for some reason Google has consented to writing >my name again. The Imaginatorium is my place of (self-)employment, And here I just assumed it was your place of self confinement. > so >I am the Chief Imaginator, but you may call me Brian. Arguing imagination among mathematikers is like arguing virtue among whores. ~v~~
From: Lester Zick on 31 Mar 2007 15:28 On 31 Mar 2007 07:29:06 -0700, "Mike Kelly" <mikekellyuk(a)googlemail.com> wrote: >On 31 Mar, 13:48, Tony Orlow <t...(a)lightlink.com> wrote: >> step...(a)nomail.com wrote: >> > In sci.math Virgil <vir...(a)comcast.net> wrote: >> >> In article <460d4...(a)news2.lightlink.com>, >> >> Tony Orlow <t...(a)lightlink.com> wrote: >> >> >>> An actually infinite sequence is one where there exist two elements, one >> >>> of which is an infinite number of elements beyond the other. >> >> >> Not in any standard mathematics. >> >> > It is not even true in Tony's mathematics, at least it was not true >> > the last time he brought it up. According to this >> > definition {1, 2, 3, ... } is not actually infinite, but >> > {1, 2, 3, ..., w} is actually infinite. However, the last time this >> > was pointed out, Tony claimed that {1, 2, 3, ..., w} was not >> > actually infinite. >> >> > Stephen >> >> No, adding one extra element to a countable set doesn't make it >> uncountable. If all other elements in the sequence are a finite number >> of steps from the start, and w occurs directly after those, then it is >> one step beyond some step which is finite, and so is at a finite step. > >So (countable) sequences have a last element? What's the last finite >natural number? 46 ~v~~
From: Lester Zick on 31 Mar 2007 15:33
On Sat, 31 Mar 2007 12:23:48 -0400, Bob Kolker <nowhere(a)nowhere.com> wrote: >Deep in your heart you want everything to be finite. That will limit >mathematics to totally up grocery bills and such like. No that will limit arithmetic and not mathematics to totaling up grocery bills and the like. >Mathematics based on infinities has made physics possible. Mathematikers still can't say what an infinity is, Bob, and when they try to they're just guessing anyway. So I suppose if we were to take your claim literally we would just have to conclude that what made physics possible was guessing and not mathematics at all. ~v~~ |