Cantor Confusion
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From: Virgil on 7 Dec 2006 15:58 In article <45780ABE.4070108(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/7/2006 4:32 AM, Virgil wrote: > > In article <4576DCFC.6040901(a)et.uni-magdeburg.de>, > > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > > >> >> Every single integer is a countable element. > >> > > >> > Since the set of integers is a subset of the set of reals, every integer > >> > is a real in any real set theory, whatever EB may claim. > >> > >> Just this is fallacious. The reals are continuous like glue. > > > > Being like glue is not a mathematically relevant quality. The Dedekind > > cut for a real, e.g., for sqrt(2), is as actual as is the rational for > > 1/2. > > > Dedekind dealt with numbers ordered like points along a line. He assumed > to consider _all_ points and _all_ rationals. This was the elusive basis > of several fallacies. See my reply this morning. The only fallacies here are by those who proclaim that ZF or NBG must have internal contradictions because they do not conform to their critic's intuitions. > > > >> Embedded genuine numbers lost their numerical address > > >> >> > Countability > >> >> > /Uncountability are properties of -sets-, not individuals. > >> >> > >> >> Do not reiterate what I know but deny. > >> > > >> > Then do not reiterate your falsehoods > >> > >> Cantor's proof (DA2) of uncountability required numbers of perfectly > >> infinite length. > > > > Cantor's first proof > > Would you please clarify what proof or paper you are referring to! The one before what you mislabel "DA2" > > You understand: Such numbers contradict common sense. > > > > Common sense is irrelevant in mathematics. > > It is only irrelevant if it contradicts to well-founded theory and has > proven wrong. In case of Cantor's transfinite numbers all putative > proofs turned out to be not correctly founded. According to EB, who confesses that he is not a mathematician. > > > >> Writing very fasr and without proofreading, I cannot guarantee correct > >> command of my English. Sometimes words or letters may be missing or > >> confused. Nevertheless, all these arguments of mine are most likely > >> flawless. > > > > Your flaws in English are excusable, your flaws in logic are not. > > I will hopefully understand at least one flaw of mine in logic, provided > you are correct. Do not hesitate pointing me to what you consider wrong > and why. Been there! Done that! Have the t-shirt!
From: Virgil on 7 Dec 2006 16:00 In article <1165495025.793999.197350(a)79g2000cws.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > > I don't know any mathematician who "pretends" an ability of > > "knowing" (what does this mean?) every integer. Who "pretends" so? > > > Virgil can imagine all natural numbers, he said. > > Regards, WM I did not claim to have personally shaken hands with each of them, as Ramanujan was rumored to have done, but I know where they live.
From: Virgil on 7 Dec 2006 16:02 In article <1165495149.718531.182430(a)j44g2000cwa.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Bob Kolker schrieb: > > > mueckenh(a)rz.fh-augsburg.de wrote: > > > > > > > > > > > Those who pretend to be able of knowing every integer and, therefore, > > > to imagine the whole actually infinite set. > > > > If there were an integer I could not imagine, there would have to be a > > least such integer. Well, it isn't 0 or 1. So the least integer I could > > not image has a predecessor. But I can imagine it. I could also imagine > > adding one to it. > > > > Contradiction. > > > > Bob Kolker > > You cannot imagine the integer [pi*10^10^100]. Why not, you just did!
From: Virgil on 7 Dec 2006 16:04 In article <45780B92.4000304(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/7/2006 4:10 AM, Virgil wrote: > > In article <4576D4C7.4070207(a)et.uni-magdeburg.de>, > > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > > > >> On 12/5/2006 10:41 PM, Virgil wrote: > >> > In article <457580FA.1030700(a)et.uni-magdeburg.de>, > >> > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > >> > >> > >> >> That there are more rationals than reals? > >> > > >> > WE do not make any such assumption. > >> > >> I perhaps meant more reals than rationals. I apologize. > >> > >> Dedekind as well as Cantor started from this idea. Cantor even > >> fabricated the notion cardinality in order to quantify the putative > >> difference in size. Considering the rationals a subset of the reals, > >> dull people conclude that there must be more reals than rationals. > > > > There certainly cannot be fewer, or even just as many, so what other > > option is open/ > > the 4th one I think that to find that 4th one must use most of a 5th.
From: Virgil on 7 Dec 2006 16:05
In article <1165495265.790747.266270(a)f1g2000cwa.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Dik T. Winter schrieb: > > > In article <1165492756.322548.255040(a)j72g2000cwa.googlegroups.com> > > mueckenh(a)rz.fh-augsburg.de writes: > > > Dik T. Winter schrieb: > > > > In article <1165421463.339178.48680(a)j44g2000cwa.googlegroups.com> > > > > mueckenh(a)rz.fh-augsburg.de writes: > > ... > > > > The set in the quantifiers you are using is not finite either. The > > > > quantifier are not over a single line, but over the set of natural > > > > numbers. > > > > > > For finite natural numbers, we have finite lines only. It is not the > > > question of a single line. Every line is finite. Therefore there is no > > > line where quantifier reversal could not be applied. > > > > But the quantifier reversal is *not* applied to individual lines, it > > is applied to the set of natural numbers. > > No. Yes! That WM does not know what is involved here does not make his ignorance correct, nor excuse it. |