Cantor Confusion
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From: Han de Bruijn on 20 Oct 2006 03:43 Dik T. Winter wrote: > In article <1161295304.522422.233980(a)b28g2000cwb.googlegroups.com> "david petry" <david_lawrence_petry(a)yahoo.com> writes: > > > > Dik T. Winter wrote: > > > In article <1161080567.156919.211680(a)i3g2000cwc.googlegroups.com> mueckenh(a)rz.fh-augsburg.de writes: > > > ... > > > > And there is no complete list of computable numbers. But they are > > > > countable. Hence the diagonal argument does not prove anything. > > > > > > You are, again, missing the essential information. There *is* such a > > > list, but it is not computable. > > > > I suggest that you are missing a key point: it all depends on what the > > definition of *is* is. > > Pray provide me with a mathematical definition. Ha! Mathematicians can't even define their most frequently used symbol, which is the equality ' = '. And that is a prerequisite for their "is". Han de Bruijn
From: Virgil on 20 Oct 2006 03:45 In article <6effb$45387c85$82a1e228$25512(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Virgil wrote: > > > In article <d6483$45372f33$82a1e228$5556(a)news2.tudelft.nl>, > > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > > > >>imaginatorium(a)despammed.com wrote: > >> > >>>I expect all the non-cranks would agree with my statement, and find it > >>>astonishing. Cranks like yourself occasionally agree with all sorts of > >>>things, more or less by accident - so what? > >> > >>Cranks, cranks .. You're clearly running out of _arguments_, aren't you? > > > > As there are no arguments that will penetrate a crankhood as profound as > > HdB's, it would hardly matter if he did run out. > > Yeah, it's a long time ago that a mathematician (Socrates) could explain > the proof of Pythagoras' Theorem to a slave, huh .. Who is to be blamed? Those who, like HdB, are slaves to their prejudices.
From: Virgil on 20 Oct 2006 03:53 In article <6cf73$45387e07$82a1e228$27759(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Dik T. Winter wrote: > > > In article <1161295304.522422.233980(a)b28g2000cwb.googlegroups.com> "david > > petry" <david_lawrence_petry(a)yahoo.com> writes: > > > > > > Dik T. Winter wrote: > > > > In article <1161080567.156919.211680(a)i3g2000cwc.googlegroups.com> > > > > mueckenh(a)rz.fh-augsburg.de writes: > > > > ... > > > > > And there is no complete list of computable numbers. But they are > > > > > countable. Hence the diagonal argument does not prove anything. > > > > > > > > You are, again, missing the essential information. There *is* such a > > > > list, but it is not computable. > > > > > > I suggest that you are missing a key point: it all depends on what the > > > definition of *is* is. > > > > Pray provide me with a mathematical definition. > > Ha! Mathematicians can't even define their most frequently used symbol, > which is the equality ' = '. And that is a prerequisite for their "is". The equal sign, "=", has many meanings, which differ depending on context, so that there cannot be one Procrustian meaning that fits all contexts. For sets A and B, A = B means that for all x, x is a member of A if and only if x is a member of B. As that definition obviously would not work in all contexts, it cannot be a universal definition.
From: Han de Bruijn on 20 Oct 2006 04:25 Virgil wrote: > In article <6cf73$45387e07$82a1e228$27759(a)news1.tudelft.nl>, > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > >>Dik T. Winter wrote: >> >>>In article <1161295304.522422.233980(a)b28g2000cwb.googlegroups.com> "david >>>petry" <david_lawrence_petry(a)yahoo.com> writes: >>> > >>> > Dik T. Winter wrote: >>> > > In article <1161080567.156919.211680(a)i3g2000cwc.googlegroups.com> >>> > > mueckenh(a)rz.fh-augsburg.de writes: >>> > > ... >>> > > > And there is no complete list of computable numbers. But they are >>> > > > countable. Hence the diagonal argument does not prove anything. >>> > > >>> > > You are, again, missing the essential information. There *is* such a >>> > > list, but it is not computable. >>> > >>> > I suggest that you are missing a key point: it all depends on what the >>> > definition of *is* is. >>> >>>Pray provide me with a mathematical definition. >> >>Ha! Mathematicians can't even define their most frequently used symbol, >>which is the equality ' = '. And that is a prerequisite for their "is". > > The equal sign, "=", has many meanings, which differ depending on > context, so that there cannot be one Procrustian meaning that fits all > contexts. > > For sets A and B, A = B means that for > all x, x is a member of A if and only if x is a member of B. Good! Now given two such members x and y. What does x = y mean? > As that definition obviously would not work in all contexts, it cannot > be a universal definition. Han de Bruijn
From: Franziska Neugebauer on 20 Oct 2006 05:32
Han de Bruijn wrote: > Virgil wrote: >> For sets A and B, A = B means that for >> all x, x is a member of A if and only if x is a member of B. > > Good! Now given two such members x and y. What does x = y mean? x = y :<-> Az(z e x <-> z e y) F. N. -- xyz |