An uncountable countable set
in [Math]
|
Prev: integral problem
Next: Prime numbers
From: imaginatorium on 22 Sep 2006 01:39 stephen(a)nomail.com wrote: > Dik T. Winter <Dik.Winter(a)cwi.nl> wrote: > > In article <eeu7fn$ti$2(a)news.msu.edu> stephen(a)nomail.com writes: > > > I do not think Tony's infinitesimals are nil-potent. > > > But see what Tony did write! > > Yes. He has apparently changed his mind, or the properties > of his infinitesimals depend on his current argument. Isn't that the crux? Crank-infinitesimals are quantities that are zero when being nonzero would cause a contradiction, but nonzero when being zero would. Brian Chandler http://imaginatorium.org
From: Han de Bruijn on 22 Sep 2006 02:55 Virgil wrote: > In article <4fd34$45123f60$82a1e228$7325(a)news2.tudelft.nl>, > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > >>stephen(a)nomail.com wrote: >> >>>Assuming that Tony's definition of infinitesimal has anything >>>to do with any standard definition of infinitesimal. :) >> >>What is "any standard definition of infinitesimal" ? > > Any of these in "non-standard analysis" as initiated by Abraham > Robinson, or "hyperreal numbers". How can "non-standard" be "standard"? Han de Bruijn
From: Han de Bruijn on 22 Sep 2006 02:58 Virgil wrote: > In article <73452$45123e3f$82a1e228$7325(a)news2.tudelft.nl>, > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > >>Virgil wrote: >> >>>In article <3a6c6$4510f00a$82a1e228$27505(a)news2.tudelft.nl>, >>> Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: >>> >>>>David R Tribble wrote: >>>> >>>>>mueckenh wrote: >>>>> >>>>>>>Nothing has changed. There is no complete set of natural numbers. Any >>>>>>>set that can be established is a finite set. Hence, the probability to >>>>>>>select a number divisible by 3 is 1/3 or very very close to 1/3. >>>>> >>>>>Virgil wrote: >>>>> >>>>>>That presumes that the allegedly finite set of naturals that can be >>>>>>constructed is nearly uniform with respect to divisibility by 3 at >>>>>>least, and probably by other numbers as well. What is the justification >>>>>>for this assumption? >>>> >>>>Wolfgang says litteraly: "_or_ very very close to 1/3". >>> >>>Which requires "_nearly uniform_ with respect to divisibility by 3". >> >>Sorry, Virgil. I don't get it. > > As usual. Other people in this group would have expressed "I don't get it" as "You are an idiot". Do you get it now? Han de Bruijn
From: Han de Bruijn on 22 Sep 2006 03:12 imaginatorium(a)despammed.com wrote: > stephen(a)nomail.com wrote: > >>Dik T. Winter <Dik.Winter(a)cwi.nl> wrote: >> >>>In article <eeu7fn$ti$2(a)news.msu.edu> stephen(a)nomail.com writes: > >>> > I do not think Tony's infinitesimals are nil-potent. >> >>>But see what Tony did write! >> >>Yes. He has apparently changed his mind, or the properties >>of his infinitesimals depend on his current argument. > > Isn't that the crux? Crank-infinitesimals are quantities that are zero > when being nonzero would cause a contradiction, but nonzero when being > zero would. Mainstream mathematics does not understand what infinitesimals are. That is because the recognition of infinitesimals would be suicidal to mainstream mathematics and its illusionary "rigour". Infinitesimals are real (or complex) non-zero numbers close to zero. They are an intermediate result in many scientific derivations which eventually lead to "exact" mathematical expressions. But not always. In probability theory, infinitesimal probabilities lead to meaningful results if questions are asked like: what is the chance that a natural number is divisible by 3. The answer is 1/3. Han de Bruijn
From: MoeBlee on 22 Sep 2006 12:19
Han de Bruijn wrote: > to mainstream mathematics and its illusionary "rigour". The rigor is in a recursive axiomatization with recursive rules of inference. You haven't shown that this is an illusion. MoeBlee |