constructible = unconstructible
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From: WM on 9 Jun 2010 12:31 On 9 Jun., 18:22, William Hughes <wpihug...(a)hotmail.com> wrote: 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 and compasses. And it is much simpler to see. 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...? Regards, WM
From: William Hughes on 9 Jun 2010 12:37 On Jun 9, 1:31 pm, WM <mueck...(a)rz.fh-augsburg.de> wrote: <snip evasion> Does the set of nodes Z= { 1 11 111 ... } contain every node in 111...? Please start your answer yes or no,
From: WM on 9 Jun 2010 14:13 On 9 Jun., 18:37, William Hughes <wpihug...(a)hotmail.com> wrote: > On Jun 9, 1:31 pm, WM <mueck...(a)rz.fh-augsburg.de> wrote: > > <snip evasion> > > Does the set of nodes > Z= > { > 1 > 11 > 111 > ... > > } > > contain every node in 111...? > > Please start your answer yes or no, No. The reason is that the actually infinite set does not exist. The resaon for this is, that, if it existed, then 111... had to exist as the last line of the list, but the list cannot have a last line. Your argument that the 1's must be spread over infinitely many lines is so obviously unmathematical nonsense that I spare further answers. Regards, WM
From: William Hughes on 9 Jun 2010 14:52 On Jun 9, 3:13 pm, WM <mueck...(a)rz.fh-augsburg.de> wrote: > On 9 Jun., 18:37, William Hughes <wpihug...(a)hotmail.com> wrote: > > > > > On Jun 9, 1:31 pm, WM <mueck...(a)rz.fh-augsburg.de> wrote: > > > <snip evasion> > > > Does the set of nodes > > Z= > > { > > 1 > > 11 > > 111 > > ... > > > } > > > contain every node in 111...? > > > Please start your answer yes or no, > > No. So in Wolkenmuekenheim there is a node in the path 111... that is not in the set of nodes Z= { 1 11 111 ... } Strange place Wolkenmuekenheim. > The reason is that the actually infinite set does not exist. > The resaon for this is, that, if it existed, then 111... had to > exist as the last line of the list. Nope, You only think this because of a classic Pink Elephant argument. After any finite number of steps you get a line from the list Look! Over There! A Pink Elephant! After an infinite number of steps you get a line from the list - William Hughes
From: WM on 9 Jun 2010 15:10
On 9 Jun., 20:52, William Hughes <wpihug...(a)hotmail.com> wrote: > On Jun 9, 3:13 pm, WM <mueck...(a)rz.fh-augsburg.de> wrote: > > > > > > > On 9 Jun., 18:37, William Hughes <wpihug...(a)hotmail.com> wrote: > > > > On Jun 9, 1:31 pm, WM <mueck...(a)rz.fh-augsburg.de> wrote: > > > > <snip evasion> > > > > Does the set of nodes > > > Z= > > > { > > > 1 > > > 11 > > > 111 > > > ... > > > > } > > > > contain every node in 111...? > > > > Please start your answer yes or no, > > > No. > > So in Wolkenmuekenheim there is a node in the path > 111... that is not in the set of nodes Even stranger is your assertion: There are nodes in the list that are not in a single line. > > The reason is that the actually infinite set does not exist. > > The resaon for this is, that, if it existed, then 111... had to > > exist as the last line of the list. > > Nope, You only think this because of a > classic Pink Elephant argument. > > After any finite number of steps > you get a line from the list and in this way you get the complete list!? > > Look! Over There! A Pink Elephant! > > After an infinite number of steps > you get a line from the list Can the complete list be constructed, with all its lines? Why can this not be done when writing all 1's in one single line? Regards, WM |