Cantor Confusion
in [Math]
|
Prev: Pi berechnen: Ramanujan oder BBP
Next: Group Theory
From: Han de Bruijn on 11 Dec 2006 05:07 Virgil wrote: > In article <1165762822.356809.126820(a)16g2000cwy.googlegroups.com>, > Han.deBruijn(a)DTO.TUDelft.NL wrote: > >>step...(a)nomail.com schreef: >> >>>Han.deBruijn(a)dto.tudelft.nl wrote: >>> >>>>Let us say that set theory is half the truth. Within set theory, any >>>>function is a special relation between commodities and products, i.e. >>>>domain and range. But the production process itself involves _labour_, >>>>hence time, and this aspect is not covered by the static set theoretic >>>>framework, where functions are reduced to "mappings" between sets. >>> >>>You can include it. You are just talking about a cost being >>>associated with a function. That is trivial to do. >> >>Exactly! In the eye of the capitalist beholder labour is identical with >>"cost". And that cost is an easy thing to incorporate. But a fact is >>that labour is not cost and not static and it involves time. And time >>is not a set. > > Is HdB so ignorant that he does not recognize velocity and acceleration > as being functions of time. If they are, why not 'labor', or anything > else that is not static, as a function of time, with domain an > appropriate set of times? Not a function of time, but time as inherent to all functions, even to functions which are a function of time. Han de Bruijn
From: Han de Bruijn on 11 Dec 2006 05:11 Virgil wrote: > In article <1165763298.462685.83360(a)73g2000cwn.googlegroups.com>, > Han.deBruijn(a)DTO.TUDelft.NL wrote: > >>step...(a)nomail.com schreef: >> >>>Do you or do you not wish to abolish any mathematics >>>that involves infinity? If you are perfectly content >>>to let others freely explore whatever they wish, then >>>why are you so aggressive? >> >>_What_ infinity. That's the question. Mainstream mathematics has mixed >>up infinity so much that it's not a sensible notion anymore. > > It is not a single notion, certainly. The 'infinity' of the 'size' of > the set of integers is quite distinct from the 'infinities' required for > the two point compactification of the reals. > > Each notion by itself, and in its appropriate context, is quite > sensible, but conflating them all into a single notin is not. Infinities can be approached only sensibly by the single notion of the good old limit concept, as it is done in standard calculus. Han de Bruijn
From: Han de Bruijn on 11 Dec 2006 05:21 stephen(a)nomail.com wrote: > Han.deBruijn(a)dto.tudelft.nl wrote: > >>Virgil schreef: > >>>In article <1165695789.274304.75780(a)80g2000cwy.googlegroups.com>, >>> Han.deBruijn(a)DTO.TUDelft.NL wrote: >>> >>>>stephen(a)nomail.com schreef: >>>> >>>>>functions, etc. as all of those things can be modelled with set theory. >>>> >>>>The topic of functions has been handled separately on my web page: >>>> >>>>http://hdebruijn.soo.dto.tudelft.nl/www/grondig/natural.htm#fd >>>> >>>>In a nutshell: the mainstream definition is narrow-minded because the >>>>whole notion of _TIME_ is lacking. >>> >>>Position, velocity and acceleration are specifically expressed as >>>functions of time, so I have no idea of what HdB is talking about. > >>Huh, no. Let f(x) = 2.x then time is involved with multiplying x by 2. > > That is your idea of time? And you think that cannot be modelled > in set theory? You are becoming increasingly irrational. Okay. Let's "model" it in set theory. Let's have your "cost" associated with f(x) = 2.x and call it C(?) = whatever. Then you have to calculate that cost and every time you do it there will be time involved with such a cost calculation. So you have to define a cost function for the cost function as well. And a cost function for the cost function of the cost function. Don't you see that this is an _explosion_ instead of a model? There is only one way to avoid a vicious circle of the kind and that is to accept that time is not a set. Han de Bruijn
From: Han de Bruijn on 11 Dec 2006 05:29 Dik T. Winter wrote: > In article <1165701092.516484.245360(a)j44g2000cwa.googlegroups.com> Han.deBruijn(a)DTO.TUDelft.NL writes: > > Really? Then you could have joined me in those _lonely_ threads about > > Chebyshev and stuff, and solve some real puzzles. There are plenty of > > the kind. > > Yeah, everybody here has ample time at his hands to solve your puzzles. > Why you always expect instant answers for your problems escapes me. > What did the mathematicians at TU Delft answer when you posed your > questions to them? (Yes, there are mathematicians there.) Huh? I don't expect instant answers. And I'm doing mathematics for fun. One aspect of having more fun is when other people want to collaborate on solving a decent puzzle. Many people in this group claim that they are genuine mathematicians. But if one comes up with a decent problem, then it seems that they are not reluctant to do some _real_ mathematics. (There are a few noteworthy exceptions to this rule, of course) Anyway, don't worry. Most of the time I can solve my own puzzles, after a while. Han de Bruijn
From: Eckard Blumschein on 11 Dec 2006 05:48
On 12/10/2006 6:43 PM, stephen(a)nomail.com wrote: > Han.deBruijn(a)dto.tudelft.nl wrote: >> step...(a)nomail.com schreef: > >>> Han.deBruijn(a)dto.tudelft.nl wrote: >>> >>> > Let us say that set theory is half the truth. Within set theory, any >>> > function is a special relation between commodities and products, i.e. >>> > domain and range. But the production process itself involves _labour_, >>> > hence time, and this aspect is not covered by the static set theoretic >>> > framework, where functions are reduced to "mappings" between sets. >>> >>> You can include it. You are just talking about a cost being >>> associated with a function. That is trivial to do. > >> Exactly! In the eye of the capitalist beholder labour is identical with >> "cost". And that cost is an easy thing to incorporate. But a fact is >> that labour is not cost and not static and it involves time. And time >> is not a set. Constructive mathematics is different from mainstream >> mathematics, precisely for that sole reason: time. Time excludes actual >> infinities as well, because they cannot be "done". > >> Han de Bruijn > > You did not provide an example of your mathematics that > incorporates time. You seem to be avoiding every question > that I ask you. Perhaps, Han is correct in principle while he should avoid the notion of time. Time includes the aspect of serial order inherent in counting. No matter how fast one counts: Something which is really infinite can never be reached because infinity is not a number but just the property to be not subject to enlargement of exhaustion. |