Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Topic: Matheology § 210
Replies: 80   Last Post: Feb 8, 2013 5:45 PM

 Messages: [ Previous | Next ]
 fom Posts: 1,968 Registered: 12/4/12
Re: Matheology § 210
Posted: Feb 5, 2013 8:21 PM

On 2/5/2013 5:49 PM, Virgil wrote:
> In article
> WM <mueckenh@rz.fh-augsburg.de> wrote:
>

>> On 5 Feb., 21:55, William Hughes <wpihug...@gmail.com> wrote:
>>> On Feb 5, 6:02 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>>>
>>> <snip>
>>>

>>>> ... one cannot even put all natural numbers in
>>>> correspondence with all natural numbers.

>>>
>>> However, one can put every natural number in
>>> correspondence with every natural number.

>>
>> One can have that by belief or decreed by the powers that be.
>> n <--> n is the finite expression of this belief. But its validity is
>> dubious because one cannot have possibly in a possible list that
>> contains every finite initial sequence of the sequence of natural
>> numbers the sequence s of every finite initial segment of the sequence
>> of natural numbers.

>
> If one cannot even justify an n to n correspondence for naturals n, then
> one has thrown out a large baby with a very little bathwater, as one has
> automatically thrown out induction as well.
>
> Induction requires that one be able to conclude that something holds for
> all n in |N.
>
> But if one cannot anything for all n in |N, no induction!
>

by finitely specified rules (as opposed to the Dirichlet
abstraction of any collection of ordered pairs satisfying
the usual constraint of well-definition).

Date Subject Author
2/5/13 mueckenh@rz.fh-augsburg.de
2/5/13 fom
2/5/13 mueckenh@rz.fh-augsburg.de
2/5/13 William Hughes
2/5/13 mueckenh@rz.fh-augsburg.de
2/5/13 William Hughes
2/5/13 Virgil
2/5/13 fom
2/5/13 Virgil
2/5/13 fom
2/6/13 mueckenh@rz.fh-augsburg.de
2/6/13 fom
2/6/13 mueckenh@rz.fh-augsburg.de
2/6/13 Virgil
2/6/13 fom
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 Virgil
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 Virgil
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/8/13 mueckenh@rz.fh-augsburg.de
2/8/13 Virgil
2/8/13 fom
2/8/13 mueckenh@rz.fh-augsburg.de
2/8/13 Michael Stemper
2/8/13 mueckenh@rz.fh-augsburg.de
2/8/13 Virgil
2/8/13 Virgil
2/7/13 Virgil
2/7/13 Virgil
2/7/13 fom
2/8/13 mueckenh@rz.fh-augsburg.de
2/8/13 Virgil
2/7/13 Virgil
2/7/13 fom
2/7/13 Virgil
2/7/13 fom
2/7/13 Virgil
2/8/13 mueckenh@rz.fh-augsburg.de
2/8/13 Virgil
2/7/13 Virgil
2/7/13 fom
2/7/13 Virgil
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 fom
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 fom
2/7/13 Virgil
2/8/13 mueckenh@rz.fh-augsburg.de
2/7/13 Virgil
2/7/13 fom
2/7/13 fom
2/7/13 fom
2/7/13 fom
2/7/13 fom
2/7/13 fom
2/6/13 Virgil
2/5/13 Virgil
2/6/13 mueckenh@rz.fh-augsburg.de
2/6/13 Virgil
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 Virgil
2/8/13 Scott Berg