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Virgil
Posts:
8,833
Registered:
1/6/11


Re: Matheology � 300
Posted:
Jul 10, 2013 2:14 PM


In article <ce9ad7bc8c1e46548e4bfe04a8ae7abc@googlegroups.com>, mueckenh@rz.fhaugsburg.de wrote:
> On Wednesday, 10 July 2013 02:18:13 UTC+2, Zeit Geist wrote: > > On Tuesday, July 9, 2013 2:25:41 PM UTC7, muec...@rz.fhaugsburg.de wrote: > > > > > > > For instance it happens in the Cantor list. Here we have as many lines as > > > we have steps in the urn. If there something unexpected can happen "at > > > omega", it can also happen in the Cantor list "at omega". But the list > > > has no line omega? Why do you think then that the urn has a step omega? > > > > > The two are very different. > > > > They deal with different objects. > > Marbles and lines? > No, both run through all natural numbers.
But WM has repeatedly claimed that, at least within WM's wild weird world of WMytheology, that there is no such thing as all natural numbers?
> That is correct, since otherwise there would be a contradiction in ZFC. But > there is no contradiction! Never!!!
At least not in ZF, though there are lots of them in WM's wild weird world of WMytheology.
> Why can a list not be like an urn? > > > > > > > > They both deal with, at some time, an aleph_0 amount of objects. > > > > But, the similarities don't go much further. > > They get further: > Every finite step of the urnprocess proves the urn is filled.
It the urn were ever filed, there would be no room for more balls i it, but there is always room for more so the urn is never filled.
> Every finite step in the rationalscomplete Cantorlist proves that the > temporariliy digonal d_1, ..., d_n is in the following lines of the list. > > "At the end" the urn is empty. True! > "At the end" the list does not contain the diagonal True! But the diagonal by then has come into existence. > > Both are exactly the same. > > Also the enumeration of the rationals is the same: > Every finite step leaves infinitely many rationals without number. > "At the end" all rationals are enumerated. True. > > > > > > > > What about the case of my Hooligan that messes up every room > > > > in one hour; and then the maid comes along and cleans each room > > > > in onehalf of an hour. > > Just the same story: Every finite step shows the number of dirty rooms is > infinite. > "At the end" all rooms are clean.
WRONG! If it takes the hooligan an hour per room, he never gets the job done, and whenever the maid starts, she will eventually catch up to him and be cleaning the room he is working on faster than he id dirtying it. > > > > > > > > You claim the maid can do it. > > I claim that the maid can do it if "all natural numbers" can be used such > that none remains, if all rationals can be enumerated and if all marbles > leave the urn.
I.e., you say the maid can do it. > > > > The Hooligan can do it, you should agree. > > The result is that never all beds are made.
Everntually, there will be at most one be in the process of being made with the rest completely made. > > > > Also, the Hooligan messes up any room before > > > > the maid cleans it. > > > > So, at noon, all rooms are cleaned.
Actually not, at least not if each room takes the same time to clean as each of its predecessors, as described above. Neither the hooigan nor the maid will ever finish unless the times needed per room form a sequence of times converging to a finite total time. > > If the devil does not respect the clause of the contract. The hooligan as > promised to kill the room maid before she has cleaned the last room. > > But the devil respects contracts. Look into Faust (Goethe): Sign in with a > drop of blood. Never devil will break a contract. He tries to cheat. But my > clause prevents me from going bancrupt.
WM was born bankrupt.
> > I did not because it is always the same. The natural numbers have a builtin > clause. They will never run out of elements.
That may be how it reads in WM's wild weird world of WMytheology, but elsewhere it only requires that each one have a successor, but, when suitable accessed, allows the set of all of them to be traversed in finite time.
For example, evaluating 'Sum 1/2^n' allows for traversing all naturals in finite time.
At least outside of WM's wild weird world of WMytheology. 



