Cantor's Diagonal?
in [Math]
|
From: zuhair on 4 Feb 2010 23:35 On Feb 4, 10:43 pm, Virgil <Vir...(a)home.esc> wrote: > In article > <f3e811e3-c4b0-4309-97b2-9d4771ed6...(a)u41g2000yqe.googlegroups.com>, > > > > > > zuhair <zaljo...(a)gmail.com> wrote: > > On Feb 4, 7:33 pm, MoeBlee <jazzm...(a)hotmail.com> wrote: > > > On Feb 4, 5:59 pm, zuhair <zaljo...(a)gmail.com> wrote: > > > > > ANY is EVERY. > > > > In a certain sense in logic, yes. So? > > > I just wanted to clarify to Virgil that in logic ANY is EVERY, > > apparently Virgil > > thought they are different, so he iterated my argument replacing ANY > > (as he > > emphasized it by writing in CAPITAL letters) instead of EVERY, so > > my reply to him was a clarification that ANY is EVERY, that's all. > > > > Do you have any remaining question or doubt that in Z set theory > > > proves there is no bijection between w and {f | f: w -> {0 1}}? > > > > MoeBlee > > > No. > > > Zuhair > > You missed my point. When there is a proof, as there is, covering ANY > instance, it automatically covers EVERY instance too. > > Thus one does not need a separate proof for both. Of course, that is trivial. Zuhair
From: Virgil on 4 Feb 2010 23:51 In article <a751f71b-5c2d-4961-b872-3ec29095faa1(a)l26g2000yqd.googlegroups.com>, zuhair <zaljohar(a)gmail.com> wrote: > On Feb 4, 10:43�pm, Virgil <Vir...(a)home.esc> wrote: > > In article > > <f3e811e3-c4b0-4309-97b2-9d4771ed6...(a)u41g2000yqe.googlegroups.com>, > > > > > > > > > > > > �zuhair <zaljo...(a)gmail.com> wrote: > > > On Feb 4, 7:33�pm, MoeBlee <jazzm...(a)hotmail.com> wrote: > > > > On Feb 4, 5:59�pm, zuhair <zaljo...(a)gmail.com> wrote: > > > > > > > ANY is EVERY. > > > > > > In a certain sense in logic, yes. So? > > > > > I just wanted to clarify to Virgil that in logic ANY is EVERY, > > > apparently Virgil > > > thought they are different, so he iterated my argument replacing ANY > > > (as he > > > emphasized it by writing in CAPITAL letters) instead of EVERY, so > > > my reply to him was a clarification that ANY is EVERY, that's all. > > > > > > Do you have any remaining question or doubt that in Z set theory > > > > proves there is no bijection between w and {f | f: w -> {0 1}}? > > > > > > MoeBlee > > > > > No. > > > > > Zuhair > > > > You missed my point. When there is a proof, as there is, covering ANY > > instance, it automatically covers EVERY instance too. > > > > Thus one does not need a separate proof for both. > > Of course, that is trivial. Then why did you not see it?
From: M. M i c h a e l M u s a t o v on 5 Feb 2010 00:44 Results 1 - 10 for CANTOR'S DIAGONAL. (0.28 seconds) Cantor's diagonal argument - Wikipedia, the free encyclopediaCantor's diagonal argument, also called the diagonalisation argument, the diagonal slash argument or the diagonal method, was published in 1891 by Georg ... en.wikipedia.org/wiki/Cantor's_diagonal_argument Google Directory - Science > Math > Logic and Foundations > Set TheoryArticle in the Platonic Realms, describing Cantor's diagonal argument that showed that 'infinite integers' can be ordered. ... www.google.com/Top/Science/Math/Logic_and.../Set_Theory/ Cantor's Diagonal ProofSimplicio: I'm trying to understand the significance of Cantor's diagonal proof. I find it especially confusing that the rational numbers are considered to ... www.mathpages.com/HOME/kmath371.htm PlanetMath: Cantor's diagonal argumentOne of the starting points in Cantor's development of set theory was his discovery that there are different degrees of infinity. ... planetmath.org/encyclopedia/CantorsDiagonalArgument.html Cantor Diagonal Method -- from Wolfram MathWorldThe Cantor diagonal method, also called the Cantor diagonal argument or Cantor's diagonal slash, is a clever technique used by Georg Cantor to show that the ... mathworld.wolfram.com/CantorDiagonalMethod.html Diagonal argument - Wikipedia, the free encyclopediaA variety of diagonal arguments are used in mathematics. "Cantor's diagonal argument" was the earliest. Cantor's diagonal argument · Cantor's theorem ... en.wikipedia.org/wiki/Diagonal_argument Kids.Net.Au - Encyclopedia > Cantor's diagonal argumentA generalized form of the diagonal argument was used by Cantor to show that for every set S the power set of S, i.e., the set of all subsets of S (here ... encyclopedia.kids.net.au/page/ca/Cantor's_diagonal_argument Simple Argument Against Cantor's Diagonal ProcedureI was also inspired by the page at <http://users.javanet.com/~cloclo/infinity.html>, entitled "Problems with Cantor's Diagonal Method and Infinity in ... homepage.mac.com/ardeshir/ArgumentAgainstCantor.html Cantor's diagonal argumentContrary to what many mathematicians believe, the diagonal argument was not Cantor's first proof of the uncountability of the real numbers, ... www.fact-index.com/c/ca/cantor_s_diagonal_argument.html Cantor's diagonal method2 posts - 1 author I just wanted to share with you a pretty formulation of Cantor's diagonal argument that there is no bijection between a set X and its power set P(X). ... www.physicsforums.com/showthread.php?t=82110 1 2 3 4 5 6 7 8 9 10 Next On Feb 4, 9:43 pm, Virgil <Vir...(a)home.esc> wrote: > In article > <f3e811e3-c4b0-4309-97b2-9d4771ed6...(a)u41g2000yqe.googlegroups.com>, > > > > > > zuhair <zaljo...(a)gmail.com> wrote: > > On Feb 4, 7:33 pm, MoeBlee <jazzm...(a)hotmail.com> wrote: > > > On Feb 4, 5:59 pm, zuhair <zaljo...(a)gmail.com> wrote: > > > > > ANY is EVERY. > > > > In a certain sense in logic, yes. So? > > > I just wanted to clarify to Virgil that in logic ANY is EVERY, > > apparently Virgil > > thought they are different, so he iterated my argument replacing ANY > > (as he > > emphasized it by writing in CAPITAL letters) instead of EVERY, so > > my reply to him was a clarification that ANY is EVERY, that's all. > > > > Do you have any remaining question or doubt that in Z set theory > > > proves there is no bijection between w and {f | f: w -> {0 1}}? > > > > MoeBlee > > > No. > > > Zuhair > > You missed my point. When there is a proof, as there is, covering ANY > instance, it automatically covers EVERY instance too. > > Thus one does not need a separate proof for both.- Hide quoted text - > > - Show quoted text -
From: zuhair on 5 Feb 2010 07:24 On Feb 5, 12:44 am, "M. M i c h a e l M u s a t o v" <marty.musa...(a)gmail.com> wrote: > Results 1 - 10 for CANTOR'S DIAGONAL. (0.28 seconds) > > Cantor's diagonal argument - Wikipedia, the free encyclopediaCantor's > diagonal argument, also called the diagonalisation argument, the > diagonal slash argument or the diagonal method, was published in 1891 > by Georg ... > en.wikipedia.org/wiki/Cantor's_diagonal_argument > > Google Directory - Science > Math > Logic and Foundations > Set > TheoryArticle in the Platonic Realms, describing Cantor's diagonal > argument that showed that 'infinite integers' can be ordered. ...www.google.com/Top/Science/Math/Logic_and.../Set_Theory/ > > Cantor's Diagonal ProofSimplicio: I'm trying to understand the > significance of Cantor's diagonal proof. I find it especially > confusing that the rational numbers are considered to ...www.mathpages.com/HOME/kmath371.htm > > PlanetMath: Cantor's diagonal argumentOne of the starting points in > Cantor's development of set theory was his discovery that there are > different degrees of infinity. ... > planetmath.org/encyclopedia/CantorsDiagonalArgument.html > > Cantor Diagonal Method -- from Wolfram MathWorldThe Cantor diagonal > method, also called the Cantor diagonal argument or Cantor's diagonal > slash, is a clever technique used by Georg Cantor to show that the ... > mathworld.wolfram.com/CantorDiagonalMethod.html > > Diagonal argument - Wikipedia, the free encyclopediaA variety of > diagonal arguments are used in mathematics. "Cantor's diagonal > argument" was the earliest. Cantor's diagonal argument · Cantor's > theorem ... > en.wikipedia.org/wiki/Diagonal_argument > > Kids.Net.Au - Encyclopedia > Cantor's diagonal argumentA generalized > form of the diagonal argument was used by Cantor to show that for > every set S the power set of S, i.e., the set of all subsets of S > (here ... > encyclopedia.kids.net.au/page/ca/Cantor's_diagonal_argument > > Simple Argument Against Cantor's Diagonal ProcedureI was also inspired > by the page at <http://users.javanet.com/~cloclo/infinity.html>, > entitled "Problems with Cantor's Diagonal Method and Infinity in ... > homepage.mac.com/ardeshir/ArgumentAgainstCantor.html > > Cantor's diagonal argumentContrary to what many mathematicians > believe, the diagonal argument was not Cantor's first proof of the > uncountability of the real numbers, ...www.fact-index.com/c/ca/cantor_s_diagonal_argument.html > > Cantor's diagonal method2 posts - 1 author > I just wanted to share with you a pretty formulation of Cantor's > diagonal argument that there is no bijection between a set X and its > power set P(X). ...www.physicsforums.com/showthread.php?t=82110 > > 1 2 3 4 5 6 7 8 9 10 Next > > On Feb 4, 9:43 pm, Virgil <Vir...(a)home.esc> wrote: > > > > > In article > > <f3e811e3-c4b0-4309-97b2-9d4771ed6...(a)u41g2000yqe.googlegroups.com>, > > > zuhair <zaljo...(a)gmail.com> wrote: > > > On Feb 4, 7:33 pm, MoeBlee <jazzm...(a)hotmail.com> wrote: > > > > On Feb 4, 5:59 pm, zuhair <zaljo...(a)gmail.com> wrote: > > > > > > ANY is EVERY. > > > > > In a certain sense in logic, yes. So? > > > > I just wanted to clarify to Virgil that in logic ANY is EVERY, > > > apparently Virgil > > > thought they are different, so he iterated my argument replacing ANY > > > (as he > > > emphasized it by writing in CAPITAL letters) instead of EVERY, so > > > my reply to him was a clarification that ANY is EVERY, that's all. > > > > > Do you have any remaining question or doubt that in Z set theory > > > > proves there is no bijection between w and {f | f: w -> {0 1}}? > > > > > MoeBlee > > > > No. > > > > Zuhair > > > You missed my point. When there is a proof, as there is, covering ANY > > instance, it automatically covers EVERY instance too. > > > Thus one does not need a separate proof for both.- Hide quoted text - > > > - Show quoted text - Most of the links are not working. Zuhair
From: Don Stockbauer on 5 Feb 2010 07:37
On Feb 5, 6:24 am, zuhair <zaljo...(a)gmail.com> wrote: > On Feb 5, 12:44 am, "M. M i c h a e l M u s a t o v" > > > > <marty.musa...(a)gmail.com> wrote: > > Results 1 - 10 for CANTOR'S DIAGONAL. (0.28 seconds) > > > Cantor's diagonal argument - Wikipedia, the free encyclopediaCantor's > > diagonal argument, also called the diagonalisation argument, the > > diagonal slash argument or the diagonal method, was published in 1891 > > by Georg ... > > en.wikipedia.org/wiki/Cantor's_diagonal_argument > > > Google Directory - Science > Math > Logic and Foundations > Set > > TheoryArticle in the Platonic Realms, describing Cantor's diagonal > > argument that showed that 'infinite integers' can be ordered. ...www.google.com/Top/Science/Math/Logic_and.../Set_Theory/ > > > Cantor's Diagonal ProofSimplicio: I'm trying to understand the > > significance of Cantor's diagonal proof. I find it especially > > confusing that the rational numbers are considered to ...www.mathpages.com/HOME/kmath371.htm > > > PlanetMath: Cantor's diagonal argumentOne of the starting points in > > Cantor's development of set theory was his discovery that there are > > different degrees of infinity. ... > > planetmath.org/encyclopedia/CantorsDiagonalArgument.html > > > Cantor Diagonal Method -- from Wolfram MathWorldThe Cantor diagonal > > method, also called the Cantor diagonal argument or Cantor's diagonal > > slash, is a clever technique used by Georg Cantor to show that the ... > > mathworld.wolfram.com/CantorDiagonalMethod.html > > > Diagonal argument - Wikipedia, the free encyclopediaA variety of > > diagonal arguments are used in mathematics. "Cantor's diagonal > > argument" was the earliest. Cantor's diagonal argument · Cantor's > > theorem ... > > en.wikipedia.org/wiki/Diagonal_argument > > > Kids.Net.Au - Encyclopedia > Cantor's diagonal argumentA generalized > > form of the diagonal argument was used by Cantor to show that for > > every set S the power set of S, i.e., the set of all subsets of S > > (here ... > > encyclopedia.kids.net.au/page/ca/Cantor's_diagonal_argument > > > Simple Argument Against Cantor's Diagonal ProcedureI was also inspired > > by the page at <http://users.javanet.com/~cloclo/infinity.html>, > > entitled "Problems with Cantor's Diagonal Method and Infinity in ... > > homepage.mac.com/ardeshir/ArgumentAgainstCantor.html > > > Cantor's diagonal argumentContrary to what many mathematicians > > believe, the diagonal argument was not Cantor's first proof of the > > uncountability of the real numbers, ...www.fact-index.com/c/ca/cantor_s_diagonal_argument.html > > > Cantor's diagonal method2 posts - 1 author > > I just wanted to share with you a pretty formulation of Cantor's > > diagonal argument that there is no bijection between a set X and its > > power set P(X). ...www.physicsforums.com/showthread.php?t=82110 > > > 1 2 3 4 5 6 7 8 9 10 Next > > > On Feb 4, 9:43 pm, Virgil <Vir...(a)home.esc> wrote: > > > > In article > > > <f3e811e3-c4b0-4309-97b2-9d4771ed6...(a)u41g2000yqe.googlegroups.com>, > > > > zuhair <zaljo...(a)gmail.com> wrote: > > > > On Feb 4, 7:33 pm, MoeBlee <jazzm...(a)hotmail.com> wrote: > > > > > On Feb 4, 5:59 pm, zuhair <zaljo...(a)gmail.com> wrote: > > > > > > > ANY is EVERY. > > > > > > In a certain sense in logic, yes. So? > > > > > I just wanted to clarify to Virgil that in logic ANY is EVERY, > > > > apparently Virgil > > > > thought they are different, so he iterated my argument replacing ANY > > > > (as he > > > > emphasized it by writing in CAPITAL letters) instead of EVERY, so > > > > my reply to him was a clarification that ANY is EVERY, that's all. > > > > > > Do you have any remaining question or doubt that in Z set theory > > > > > proves there is no bijection between w and {f | f: w -> {0 1}}? > > > > > > MoeBlee > > > > > No. > > > > > Zuhair > > > > You missed my point. When there is a proof, as there is, covering ANY > > > instance, it automatically covers EVERY instance too. > > > > Thus one does not need a separate proof for both.- Hide quoted text - > > > > - Show quoted text - > > Most of the links are not working. > > Zuhair |