
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 courseofvalues. > > >> 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

