constructible = unconstructible
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From: William Hughes on 9 Jun 2010 11:33 On Jun 9, 12:17 pm, WM <mueck...(a)rz.fh-augsburg.de> wrote: > On 9 Jun., 17:01, William Hughes <wpihug...(a)hotmail.com> wrote: > > > > > > antidiagonal 111... of the list > > > > 000... > > > 1000... > > > 11000... > > > 111000... > > > ... > > > > would have been written down (covered) by writing (covering) all > > > paths of the form 111...111000... of the set Y. Can that happen? > > > Yes. The anti diagonal is *covered* by the set Y but is > > not *in* the set Y. > > That is wrong by the linearity of the set. If all 1's of 111... are in > the list, then either all can be in one line or they cannot be in one > line. > > Agreed? > > If they are in one line, then 111... is in the list. > > If they cannot be in one line, then there must be at least two lines > containing all 1's. Correct to this point. (Note however, "at least". Indeed you need an infinite number of lines to contain all 1's) > That means, there must be at leat two 1's of > 111... that cannot be in one common line. No. This does not follow. Your turn Does the set of nodes Z= { 1 11 111 ... } contain every node in 111...? Please begin your answer yes or no. - William Hughes
From: WM on 9 Jun 2010 11:55 On 9 Jun., 17:33, William Hughes <wpihug...(a)hotmail.com> wrote: > On Jun 9, 12:17 pm, WM <mueck...(a)rz.fh-augsburg.de> wrote: > > > > > > > On 9 Jun., 17:01, William Hughes <wpihug...(a)hotmail.com> wrote: > > > > > antidiagonal 111... of the list > > > > > 000... > > > > 1000... > > > > 11000... > > > > 111000... > > > > ... > > > > > would have been written down (covered) by writing (covering) all > > > > paths of the form 111...111000... of the set Y. Can that happen? > > > > Yes. The anti diagonal is *covered* by the set Y but is > > > not *in* the set Y. > > > That is wrong by the linearity of the set. If all 1's of 111... are in > > the list, then either all can be in one line or they cannot be in one > > line. > > > Agreed? > > > If they are in one line, then 111... is in the list. > > > If they cannot be in one line, then there must be at least two lines > > containing all 1's. > > Correct to this point. (Note however, "at least". Indeed you need > an infinite number of lines to contain all 1's) That can be so or not. But if you claim that infinitely many are needed, then it should be possible for you, to find at least two of those, which are needed. > > That means, there must be at leat two 1's of > > 111... that cannot be in one common line. > > No. This does not follow. You claim infinitely many lines were required, but you cannot even find two. We should fix that result. > > > Your turn You claim that the list 1 11 111 .... contains all 1's of 111..., but that no single line contains all 1's of 111... . This is obviously as impossible as squaring the circle by ruler compasses. And it is much simpler to see. I proved it in my recent contribution. Your claim however is necessary for set theory. Therefore set theory is wrong. But here I have an argument that might be intelligible to you: Write the above list, but extinguish every previous line after you have written the next line. Then the "list" shrinks to a single line. Do you think that this single line contains all 1's of 111...? In other words: Do you believe that N is constructible? If yes, why must we extinguish the previous lines in order to catch all 1's in a single line? If no, then also no Cantor-list can be constructed. No proof of uncountability is then possible. No counting beyond final numbers is possible and sensible. Regards, WM
From: William Hughes on 9 Jun 2010 12:07 On Jun 9, 12:55 pm, WM <mueck...(a)rz.fh-augsburg.de> wrote: <snip> > > Your turn > <snip evasion> Does the set of nodes Z= { 1 11 111 ... } contain every node in 111...? Please begin your answer yes or no. - William Hughes
From: WM on 9 Jun 2010 12:16 On 9 Jun., 18:07, William Hughes <wpihug...(a)hotmail.com> wrote: > Does the set of nodes > Z= > { > 1 > 11 > 111 > ... > > } > > contain every node in 111...? It contains all nodes that are contained in one single line, if you write infinitey long and delete, when writing a line, always the previous one. Regards, WM
From: William Hughes on 9 Jun 2010 12:22
On Jun 9, 1:16 pm, WM <mueck...(a)rz.fh-augsburg.de> wrote: > On 9 Jun., 18:07, William Hughes <wpihug...(a)hotmail.com> wrote: > > > Does the set of nodes > > Z= > > { > > 1 > > 11 > > 111 > > ... > > > } > > > contain every node in 111...? > <snip evasion> Please start your answer yes or no, - William Hughes |