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.