How Wide Do All The Possible Computed Digit Sequences Go?
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From: |-|ercules on 28 Jun 2010 18:44 "Joshua Cranmer" <Pidgeot18(a)verizon.invalid> wrote ... > On 06/28/2010 01:25 AM, |-|ercules wrote: >> GET IT RIGHT! LEARN TO make your insults CLEAR and SPECULATIVE! >> A rabbit possum will haunt YOU *IN* your nighties! > > Actually, one of the definitions of "haunt" is (according to my > dictionary) "to visit frequently." If you consider your nightmares to be > a place for your mind to dwell, it is not hard for a rabid (not rabbit, > rabid) possum to haunt them. I don't mind people missing the point of my posts but NOBODY, NOBODY denegrades the rabbit possum outside of the realm of dwelling minds meanwhile denegrading my use of a living language with uncouth derelict terms mmmkay! Herc
From: herbzet on 28 Jun 2010 22:27 George Greene wrote: > And you REALLY DON'T want to say lim S for a list S, because > that puts the burden OF DEFINITION IN FORMAL LANGUAGE back > ON YOU instead of on Herc. > Herc in any case is NOT going to concede that he is using > limits, and that what is really going on here is that certain > kinds of infinite collections can approach a limit WITHOUT > actually CONTAINING it. Indeed, the set of, e.g., the rational numbers has vastly more limit points than it has elements ...
From: David Bernier on 7 Jul 2010 06:30
Transfer Principle wrote: > On Jun 24, 10:57 pm, David Bernier<david...(a)videotron.ca> wrote: >> Tim Little wrote: >>> True, but irrelevant to Cantor's proof (which uses the ordinary >>> mathematical meaning) and everything else he's ranting about though. >> I have this analogy between chess concepts and mathematics concepts >> which occurred to me not long ago. >> In chess, there are the Laws of chess. This I associate >> to formal deductions in FOL ZFC. Anybody can check >> a proof of Cantor's result that there is no bijection >> between omega and P(omega); this would be >> tedious and probably un-enlightening. > > But as not everyone is forced to play chess, not everyone > is forced to use FOL+ZFC. > > Also, it's possible to know all the rules of chess, and > nonetheless choose not to play it, or believe that the game > isn't worth playing. Yet the "chess players" in this thread > (the ZFC Herc-"religionists") insist that Herc doesn't know > how to play chess (doesn't understand FOL+ZFC) merely > because he doesn't want to play it (want to use FOL+ZFC). > > It's possible to know all the rules of a game and still not > choose to play it, but this possibility has escaped most > posters in this thread. > > This is how I interpret Bernier's analogy. I was thinking of first order set theory (ZFC), without any defined terms; for example, the following is a standard defined term: _ordered_pair_ . The ordered pair (x, y) := { {x}, {x, y} } . (Kuratowski def.) Reference: < http://en.wikipedia.org/wiki/Ordered_pair> Getting rid of all defined terms, one is left with bare set theory. Then a well-formed formula (or just formula) with the free variable f expressing: "f is a function from omega to P(omega)" becomes long and unwieldy. Once I wrote a computer program to re-write formulas so that no defined terms were used: only element of and logical connectives and quantifiers were allowed. Then " x is the Real numbers" was re-written as a very long formula. So my point is, even with the Laws of ZFC, non-trivial formulas are often unwieldy when all is re-written with no use of defined terms. David Bernier |