Cantor Confusion
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From: Virgil on 6 Oct 2006 15:40 In article <1160122165.927132.128920(a)h48g2000cwc.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > In this case omega is enforced. That is kind of forcing. And when we > split the balls escaping from vase A by collecting them in vases B and > C at equal shares, then we may speak of the method of forking. > > Forcing forking shows that the assumption of the existence of omega > does not yield consistent results. That has nothing to do with > intuition. We see that half of all balls are in B and half are in C at > noon. But if C did not exist, then all balls were in B. It is simply > ridiculous what kind of logic set theorist must endorse. If C did not exist and "Mueckenh" still insists that half the balls go into C, then it is "Mueckenh"'s logic that is flawed, not whose who deduce things from ZF or NBG.
From: Virgil on 6 Oct 2006 15:48 In article <1160130133.754004.185440(a)c28g2000cwb.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > I am talking of the substitute for actual infinity, which Cantor > introduced. omega is not only the set N but also the cardinal number of > this set. Actually "omega" is an ordinal, not a cardinal. Aleph_0 is the corresponding cardinal. > > > What does that have to do with this? What is "a > > number like omega", anyway? > > According to Cantor it is a whole number larger than any natural > number. It is my first aim to show that omega is not a number. That depends very strongly on what one chooses to allow as a being a number. It is certainly not a natural number, but there are lots of things that are called numbers which are not natural numbers. > > > Do you mean a limit ordinal? Again: what > > that has to do with the thinker I wrote? How does one eternal being go > > about being "omega" years old? > > It has to do with the actual existence of infinity. It has to do with > the possibility to surpass this infinity by a larger one. One does not need more than one of size of infinity in order to consider the lifetime of an immortal.
From: Virgil on 6 Oct 2006 15:50 In article <1160131022.114767.303340(a)k70g2000cwa.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > The original character is Tristram Shandy of a novel by L. Sterne who > needs one year to describe one of his days. (Let him start at birth.) > "If he lives forever, no day of his life remains unwritten" is the > assertion of single-eyed set theorists. More than 99% of his life > remain unwritten is the truth. Even if he lives forever. To teach that > to math students would be more important. And if Tristram Shandy lives forever, there is no single day that he will not record. At least until he runs out of paper on which to record it.
From: Virgil on 6 Oct 2006 15:55 In article <1160131605.270965.172370(a)m7g2000cwm.googlegroups.com>, "Albrecht" <albstorz(a)gmx.de> wrote: > Virgil schrieb: > > > In article <1160048322.932236.254800(a)b28g2000cwb.googlegroups.com>, > > "Albrecht" <albstorz(a)gmx.de> wrote: > > > > > Virgil schrieb: > > > > > > > In article <1160033333.428361.122020(a)h48g2000cwc.googlegroups.com>, > > > > "Albrecht" <albstorz(a)gmx.de> wrote: > > > > > > > > > MoeBlee schrieb: > > > > > > > > Give me your axiomatization that is rich enough for ordinary > > > > > > calculus, > > > > > > and with a mathematical definition of 'constructible', and such > > > > > > that > > > > > > every real number is constructible. Then we'll talk about that. > > > > > > > > > > Do we really need such an axiomatisation? 99% of mathematics was done > > > > > without it. And was done right. > > > > > > > > But 99% is not good enough, in mathematics. > > > > > > No, todays math needs 1000%. As it needs infinite^2 and more objects. > > > > Actually, it is only A.S.S. who asks for 1000%. Mathematicians would > > readily accept 100%, but not 99%. > > > > > > I'm sure: mathematicians have not 1%. To be exact: They never have any > % of math as Goedel had shown. Math is infinite. The totality of mathematics extant may, in sufficient time, exceed any finite limit in size, but at present the amount of it extant is still finite, though too great for any one person to comprehend all of it.
From: Virgil on 6 Oct 2006 15:57
In article <1160131792.639443.169530(a)i42g2000cwa.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > William Hughes schrieb: > > > Note the question was very carefully posed so it was not > > "Can X write about all his days?", but "Can X write about > > every single day?". > > There is the answer 1) There is no day which will not be written. > There is the answer 2) There is a day which will not be written namely > the present day. > > Both answers contradict each other. > > Regards, WM The present day, which is always today, will be written on a future day, which is not yet, but will be. |