details re Z-R |- PA consistent
in [Logic]
|
Prev: geometry template for infinite-line-ray to precision define infinite-number in Peano Axioms #627 Correcting Math
Next: The Necessary vs Contingent Distinction
From: FredJeffries on 13 Aug 2010 05:13 On Aug 11, 9:55 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > > Say a sci.math states that a finite natural number is one which > has a real-world physical application. I can then recast this > definition as, "n is a finite natural number iff when asked 'Is n a > natural number?' at his birth, Y-V will answer 'yes' sometime > prior to his death." So you do not consider RSA numbers to be "a real-world physical application"?
From: FredJeffries on 13 Aug 2010 05:31 On Aug 11, 9:37 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > On Aug 7, 7:49 am, FredJeffries <fredjeffr...(a)gmail.com> wrote: > > > On Aug 6, 9:14 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > > > I've been thinking about how to come up with an axiom that > > > states the existence of _TO's_ infinitesimals. > > > And we need a theory other than ZF, and an axiom other > > > than the ultrafilter axiom, to obtain TO's infinitesimals. > > So you are looking for the Magic Bullet? That entity so small that any > > finite number of them strung together is infinitesimal but infinitely > > many together have a finite size? The solution to "since the sum from > > 1 to n of 1/n is 1, take the limit as n goes to infinity"? A uniform > > distribution for the natural numbers? > > I don't know how to give you a formalization, but I have thought of a > > real world application: > > Let's call our magic bullet M and we know that an omega sequence of M > > stuck together has size 1 (sum for i = 1 to infinity of M yields 1) . > > In thinking about this, I just realized something here. What does it > mean for infinitesimals like M to be "stuck together"? > I didn't say that the infinitesimals were stuck together. I said that the magic bullets (each of which has infinitesimal size) are stuck together.
From: FredJeffries on 13 Aug 2010 10:58 On Aug 11, 9:55 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > > The mathematician Y-V has been frequently mentioned as a > counterexample to my claim that finitists are called "cranks." So, > rather than ask why Herc, HdB, WM are called "cranks" and not > Y-V (since no satisfactory answer can ever be given), I decide > that I will take _advantage_ of this fact that Y-V is a finitist who > isn't called a "crank." > > To take advantage of this, when a sci.math finitist is asked to > give a coherent definition (as the inability to give such a definition > is one often-cited reason for assigning a "crank" label), I can > jump in and give a definition in terms of Y-V. > > Say a sci.math states that a finite natural number is one which > has a real-world physical application. I can then recast this > definition as, "n is a finite natural number iff when asked 'Is n a > natural number?' at his birth, Y-V will answer 'yes' sometime > prior to his death." Then this will become a non-"crank" > definition since it's given in terms of the non-"crank" Y-V. Sigh. You really don't get the Yessenin-Volpin story, do you? And I feel somewhat responsible since I'm the one who told it to you...
From: Marshall on 13 Aug 2010 11:00 On Aug 13, 7:58 am, FredJeffries <fredjeffr...(a)gmail.com> wrote: > > Sigh. You really don't get the Yessenin-Volpin story, do you? And I > feel somewhat responsible since I'm the one who told it to you... He does that on purpose, to irritate people. Marshall
From: MoeBlee on 13 Aug 2010 12:04
On Aug 12, 5:59 pm, "Ross A. Finlayson" <ross.finlay...(a)gmail.com> wrote: > yeah Moe [...] If you're going to address me directly, it would be nice for you to at least write other than ungrammatical, incoherent messes. MoeBlee |