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Topic: Infinity: The Story So Far
Replies: 16   Last Post: Mar 7, 2014 8:31 AM

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Peter Percival

Posts: 2,623
Registered: 10/25/10
Re: Infinity: The Story So Far
Posted: Mar 6, 2014 7:40 AM
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Virgil wrote:
> In article <lf83m8$tqh$1@news.albasani.net>,
> Peter Percival <peterxpercival@hotmail.com> wrote:
>

>> Virgil wrote:
>>> In article <4cfd9bb3-5708-4ed7-9285-e2735a4fcd85@googlegroups.com>,
>>> mueckenh@rz.fh-augsburg.de wrote:
>>>

>>>> But he claimes that the Peano-axioms supply the natural numbers of formal
>>>> mathematics. So the natural numbers of formal mathematics are:
>>>> 1, -10, 100, -1000, ...

>>>
>>> Only in wierd places like WM's wild weird world of WMytheology.
>>> Elsewhere, the successor operation is denoted by adding one.

>>
>> I don't think that is correct.

>
>
> In abstract induction it need not be, but in the standard set of
> naturals, which is what WM is arguing about, it most assuredly is.


But what are the naturals defined to be? If it's "things satisfying
Peano's axioms" then 1, -10, 100, -1000, ... (with the appropriate S) do
the job.

--
Madam Life's a piece in bloom,
Death goes dogging everywhere:
She's the tenant of the room,
He's the ruffian on the stair.



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