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Topic: mathematical infinite as a matter of method
Replies: 25   Last Post: May 4, 2013 11:24 PM

 Messages: [ Previous | Next ]
 Graham Cooper Posts: 4,495 Registered: 5/20/10
Re: mathematical infinite as a matter of method
Posted: May 3, 2013 8:54 PM

On May 4, 10:03 am, fom <fomJ...@nyms.net> wrote:
> On 5/3/2013 5:03 PM, Graham Cooper wrote:
>
>
>
>
>
>
>
>
>

> > On May 3, 8:15 pm, fom <fomJ...@nyms.net> wrote:
> >> On 5/3/2013 2:43 AM, Graham Cooper wrote:
>
> >>> Its not possible to test Equality by Extension in the inf. case.
>
> >> That is correct Herc.
>
> >> On the other hand,  it is not possible to interpret
> >> the universal quantifier as a universal statement if
> >> it is interpreted as a course-of-values.

>
> >> Aristotle wrote this.  It is ignored by a certain
> >> contingent of the mathematical community who merely
> >> argues on the basis of beliefs concerning infinity.

>
> >> You know well that any computer system balances
> >> choices that affect performance.  Relational databases
> >> run faster on logic chips optimized for integral
> >> arithmetic as opposed to floating point.  The analogy
> >> applies here.

>
> >> Brouwer had been clear concerning how the effectiveness
> >> of working with finite sets differed from working
> >> with infinite sets.  But, the reason infinity enters
> >> mathematics is because it is how the identity relation
> >> is extended to convey the geometric completeness of a
> >> line when used to represent the real number system.

>
> >> Infinity does not arise because of testability.  It
> >> arises because of the nature of the identity relation.

>
> > If there are more SETS in ZFC than FORMULA in ZFC
> > (David C Ullrich)

>
> > ZFC FORMULA   |   ZFC SETS
>
> > 1  ___________ a        i
> > 2  ___________ b    p          q    r
> > 3  ___________ c            j   n
> > 4  ___________ d   s      t    k           u  v
> > 5  ___________ e       z      w
> > ...

>
> > THEN WHAT DO YOU MEAN BY ...
>
> > A SET OF ZFC ?
>
> I actually agree with you somewhat here.
>
> Nevertheless, if one restricts to countable
> models, then it is clear that there must be
> real numbers not represented.  In particular,

No, you're entitled to that view but hundreds of people say it is NOT
clear.

GIVEN AN INFINITE LIST
YOU CAN CONSTRUCT A MISSING REAL

is simply wrong! there is no turing machine that can do that and
halt.

------------------------------------------------------

Given there are oo choices for the 1st selected row of the list
and only 10 digits to select from
Every possible digit can appear at

LIST_1_1

by the Pigeon Hole Principle.

+------------>
| 0. 1 ..
| ...
|
| 0. 2 ..
|
| ...
|
| 0. 3 ..
|
| ..
|
| 0. 4 ..
|
| ..
|
| 0. 5 ..
|
| ..
|
| 0. 6 ..
|
| ...
|
| 0. 7 ..
|
| ...
|
| 0. 8 ..
|
| ..
|
| 0.9 ..
|
| ..
|
| 0. 0 ..
|
|
|
|
|
V

INFINITE CHOICES
10 OPTIONS

By the P.H.P. the

DIAG(1) = [ 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 ]

NEGATING DIAG(1)

6 --> 4

changes the Diagonal
which gives you a different permutation.

CHANGE PERMUTATION <=> CHANGE DIGIT ON DIAGAONAL

--------------

When you CHANGE THE DIGITS OF THE DIAGONAL

1 - at - a - time

AT EVERY STEP OF THE ALGORITHM

You have the SAME LIST (permuted)

----------------

No one in their right mind would say:

+--------->
| 0.134...
| 0.224...
| 0.563...
| ...
v

0.123... is missing

because:

0.5., is on the list CHANGE TO 1
0.X3... is on the list CHANGE TO 2
0.XX4... is on the list CHANGE TO 3

but by sorting the list:

+--------->
| 0.563...
| 0.134...
| 0.224...
| ...
v

YOU DO CLAIM 0.123... is missing!

IT's just the DIAGONAL of list 1!

-----------

So you claim

ALL ANTIDIAGONALS OF ALL PERMUTATIONS ARE MISSING!

+--------->
| 0. 1 [3] 4...
| 0. 2 2 [4]...
| 0. [5] 6 3...
| ...
v

SO THAT PATH [5] [3] [4]

CAN BE INVERTED!

to 0.123...

----------------------------

So you claim the DIAGONAL is CLEARLY ABSENT TOO!

by the Pigeon Hole Principle!

Herc

--
www.BLoCKPROLOG.com

Date Subject Author
4/21/13 fom
4/21/13 Virgil
5/2/13 Hercules ofZeus
5/2/13 fom
5/2/13 Virgil
5/3/13 Graham Cooper
5/3/13 fom
5/3/13 Brian Q. Hutchings
5/3/13 Graham Cooper
5/3/13 fom
5/3/13 Graham Cooper
5/3/13 fom
5/3/13 fom
5/4/13 Graham Cooper
5/3/13 Graham Cooper
5/3/13 fom
5/3/13 Graham Cooper
5/4/13 fom
5/4/13 Graham Cooper
5/4/13 fom
5/4/13 Graham Cooper
5/4/13 fom
5/4/13 Graham Cooper
5/4/13 fom
5/4/13 Graham Cooper
5/3/13 Graham Cooper