Virgil
Posts:
4,482
Registered:
1/6/11
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Re: WMatheology � 154: Consistency Proof!
Posted:
Nov 25, 2012 5:08 PM
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In article
<4843b730-45be-4d95-a839-038f89b4c95b@n5g2000vbk.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 25 Nov., 21:36, Virgil <vir...@ligriv.com> wrote:
>
> > Mathematics, before it can find a limit, must define what is expected of
> > that limit,
>
> Analysis has been invented to analyze seqeunces and to *find* limits.
Actually it was also invented to show that sometimes no limit exists!
>
> > and in sensible mathematics the limit of a sequence of real
> > numbers, if it exists, and the limit of a sequence of sets, if it also
> > exists, will never be the same thing.
>
> Therefore set theory should be exorcized from mathematics.
Because differentiation and integration give different results, would WM
force mathematics to "exorcize" one of them?
> >
> > And furthermore, the sequence of real number numerals that WM is harping
> > about does not exist as a real number numeral at all.
>
> The sequence of digits 0, 1, 0, 1, 0, 1, ... does exist as well as the
> set of indexed digits {0_1, 1_2, 0_3, 1_4. ...} and the decimal
> representation ...010101 with value oo.
The sequence of digits gives the set of digits {1,0},
Any sequence of digits preceded by a point is less than 1.
Besides which, in standard decimal representations, any real number that
can be decimally represented has at most two distinct representations,
while your claimed "oo" number would have to have uncountably many
"decimal" representations if it were allowed to have any at all.
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