Cantor Confusion
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From: Franziska Neugebauer on 4 Dec 2006 10:43 mueckenh(a)rz.fh-augsburg.de wrote: > Franziska Neugebauer schrieb: >> mueckenh(a)rz.fh-augsburg.de wrote: >> > So you can construct the set of all real numbers (of the interval >> > [0, 1] in binary representation) by: >> > >> > 0.0 >> > 0.1 >> > 0.01 >> > 0.11 >> > ... >> > >> > This set is countable. >> >> 1/3 is missing. > > Of course. It is not a potentially infinte sequence. 1/3 is not a sequence at all. It is a rational number. F. N. -- xyz
From: stephen on 4 Dec 2006 11:02 mueckenh(a)rz.fh-augsburg.de wrote: > stephen(a)nomail.com schrieb: >> mueckenh(a)rz.fh-augsburg.de wrote: >> >> > Dik T. Winter schrieb: >> >> >>Do they define sets as allowed to grow? Not in the quote you supply. >> >> There they talk about set valued variables that can grow. >> >> > No. X and Y do not grow, they remain "X" and "Y". The set they denote >> > does grow. The number of EC states may be n. "n" does not grow. The >> > number denoted by "n" does grow. >> >> What do you mean by the 'the number denoted by "n" does grow'? >> Currently the number of EC states is 25. In a month it will be 27. >> Does that mean 25 is going to grow into 27? Will 25 no longer exist? >> Or will 25 now mean 27? What do you mean by 'the number denoted by "25" does >> grow'? > It is only a matter of definition and in principle no reason for > quarrel. But it is amusing to see ho set theorists insist on the > complete and actual existence of the sets of numbers. Of course 25 will > not switch to 27 but the number of states will switch from 25 to 27. > That's all. Only by this notion we can talk of growing sets and > introduce the notion of potential infinity. So the number denoted by "n" does not grow? You seem to be switching your position. >> >> The idea that 25 is ever going to be anything but 25 is absolutely ridiculous. >> The idea that a set ever changes is equally ridiculous. > No. Compare Fraenkel et all. They talk about to look at the universe of > all sets not as a fixed entity but as an entity capable of "growing". > What they understand and how this growing can take place has lead to > many misunderstandings by underinformed mathematicians. But however one > may interpret their sentence. The universe of all sets can change, to > put it cautiously. That is not at all ridiculous. > Regards, WM Nobody but you has talked about "growing" sets. Sets, like numbers, do not grow. You, like many other people who do not understand set theory, think of sets as mutable objects, that change as we perform operations on them. This is akin to thinking that numbers change when we perform addition. If I add 3 to 7, neither 3 or 7 changes. Stephen
From: Lester Zick on 4 Dec 2006 12:14 On Sun, 3 Dec 2006 22:19:09 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: [. . .] >Speaking of admitting errors, when will you admit your myriad errors? When you admit yours perchance? ~v~~
From: Lester Zick on 4 Dec 2006 12:15 On Sun, 3 Dec 2006 22:29:09 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >Eckard Blumschein wrote: >> On 11/22/2006 12:16 AM, David Marcus wrote: >> >> > It is hard to be always wrong. >> >> In what, according to your opinion, WM is not wrong? > >I believe I was referring to the fact that you agreed with Virgil, and >hence might be right about something. However, WM does, now and then, >say something that is correct, but generally immediately says something >that is absurd. And thus is shortlisted for admission as a mathematiker in good standing. ~v~~
From: imaginatorium on 4 Dec 2006 12:35
stephen(a)nomail.com wrote: > mueckenh(a)rz.fh-augsburg.de wrote: > > > Dik T. Winter schrieb: > > >>Do they define sets as allowed to grow? Not in the quote you supply. > >> There they talk about set valued variables that can grow. > > > No. X and Y do not grow, they remain "X" and "Y". The set they denote > > does grow. The number of EC states may be n. "n" does not grow. The > > number denoted by "n" does grow. > > What do you mean by the 'the number denoted by "n" does grow'? > Currently the number of EC states is 25. In a month it will be 27. > Does that mean 25 is going to grow into 27? Will 25 no longer exist? > Or will 25 now mean 27? What do you mean by 'the number denoted by "25" does > grow'? > > The idea that 25 is ever going to be anything but 25 is absolutely ridiculous. > The idea that a set ever changes is equally ridiculous. Obviously not a FORTRAN programmer... SUBROUTINE CHANGE(A, B) IF(A .EQ. 25) A = B RETURN END Now try: CALL CHANGE(25, 17) Brian Chandler http://imaginatorium.org |