Can N be constructed?
in [Logic]
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From: WM on 9 Jun 2010 13:59 If this question is denied, then it is impossible to construct a Cantor list and it is impossible to count beyond any finite number. If N can be constructed, then the elements n can be constructed in the unary system as an infinite sequence of finite sequences of 1's (i.e. as a list of finite sequences) 1 11 111 .... This list contains all 1's that are contained in 111... The claim is that no line contains all these 1's. This claim can be disproved. Proof: Construct the above list, but remove always line number n after having constructed the next line number n + 1. Then the list shrinks to a single line but this single line contains the same as the list because never anything is removed that has not been added before to an existing line. This result appears paradoxical. But the only paradoxical is the assumption that infinity can be finished (and that thousands of rather intelligent people have been believing that for more than 100 years). Regards, WM
From: William Hughes on 9 Jun 2010 15:08 On Jun 9, 2:59 pm, WM <mueck...(a)rz.fh-augsburg.de> wrote: > If this question is denied, then it is impossible to construct a > Cantor list and it is impossible to count beyond any finite number. > > If N can be constructed, then the elements n can be constructed in the > unary system as an infinite sequence of finite sequences of 1's (i.e. > as a list of finite sequences) > > 1 > 11 > 111 > ... > > This list contains all 1's that are contained in 111... > The claim is that no line contains all these 1's. This claim can be > disproved. > > Proof: Construct the above list, but remove always line number n after > having constructed the next line number n + 1. > 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. The line you get after an infinite number of steps is not a line from the list. > Then the list shrinks to a single line Yes the line 111... > but this single line contains > the same as the list because never anything is removed that has not > been added before to an existing line. > > This result appears paradoxical. Nope. 111... does contain "the same as the list" - William Hughes
From: WM on 9 Jun 2010 15:16 On 9 Jun., 21:08, William Hughes <wpihug...(a)hotmail.com> wrote: > On Jun 9, 2:59 pm, WM <mueck...(a)rz.fh-augsburg.de> wrote: > > > > > > > If this question is denied, then it is impossible to construct a > > Cantor list and it is impossible to count beyond any finite number. > > > If N can be constructed, then the elements n can be constructed in the > > unary system as an infinite sequence of finite sequences of 1's (i.e. > > as a list of finite sequences) > > > 1 > > 11 > > 111 > > ... > > > This list contains all 1's that are contained in 111... > > The claim is that no line contains all these 1's. This claim can be > > disproved. > > > Proof: Construct the above list, but remove always line number n after > > having constructed the next line number n + 1. > > The line you get after an infinite number of steps is not > a line from the list. But the list you get after an infinite number of steps (with no predecessor line removed) does not contain that line? > > > Then the list shrinks to a single line > > Yes the line 111... And this line is different from the line you get when not removing its predecessors? > > > but this single line contains > > the same as the list because never anything is removed that has not > > been added before to an existing line. > > > This result appears paradoxical. > > Nope. 111... does contain "the same as the list" But if the complete list is constructed, then that line which contains "the same as the list", is not constructed? It comes into being only by distinguishing its predecessors??? You believe in some kind of interference like light and light gives darkness? Regards, WM
From: George Greene on 9 Jun 2010 15:20 On Jun 9, 1:59 pm, WM <mueck...(a)rz.fh-augsburg.de> wrote: and that is an utter tragedy in itself. I've only been back for two weeks. Is it my fault? Should I have stayed gone? Would that have prevented the return of the locusts?
From: George Greene on 9 Jun 2010 15:25
Can WM be reconstructed? Seriously, a question about "constructing N" is just bullshit on its face. He is not going to define "to construct", and even if he could, it wouldn't matter. He will have to concede that individual elements of N (each and EVERY n in N) CAN be constructed -- ALL of them. Whether or not the whole is also "constructible" IS NOT something that NEEDS to be ANSWERED --- it CAN just be STIPULATED --- you can have an axiom EITHER WAY YOU LIKE. |