Obections to Cantor's Theory (Wikipedia article)
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From: malbrain on 28 Jul 2005 22:36 Dik T. Winter wrote: > In article <1122567294.560463.170070(a)g49g2000cwa.googlegroups.com> malbrain(a)yahoo.com writes: > > Dik T. Winter wrote: > ... > > > > Well, the OBVIOUS answer to your question is, "I'm talking about C" > > > > However, I'm not that vulgar. I tend to translate discussions into C > > > > because I find it to be more universally understood than java. karl m > > > > > > So what? When someone talks about java with "unbounded" standard types, > > > what is the point stating that C does not have "unbounded" standard types? > > > > How is the length of an integer determined by a java program running on > > the virtual-java-machine? karl m > > Yes, what are you trying to tell? I think you would be better off when you > get back on your chair. Sorry, but I submitted in my position to seniority. I'll try my best to cover my new role. If we can get the program to determine the length of the standard integer type we can map to the C INT_MAX declaration during execution. karl m
From: Poker Joker on 28 Jul 2005 23:02 "Virgil" <ITSnetNOTcom#virgil(a)COMCAST.com> wrote in message news:ITSnetNOTcom%23virgil-0B4339.01230428072005(a)comcast.dca.giganews.com... > In article <iUXFe.297$Zh.52(a)tornado.rdc-kc.rr.com>, > "Poker Joker" <Poker(a)wi.rr.com> wrote: > >> "Daryl McCullough" <stevendaryl3016(a)yahoo.com> wrote in message >> news:dc9f0t03cj(a)drn.newsguy.com... >> >>> >Robert Low said: >> >>> > >> >>> >> OK, so how many elements are there in the set of all finite >> >>> >> natural numbers? >> > >> > Tony replied. >> > >> >>>>Some finite, indeterminate number. >> > >> > That is an out-and-out contradiction. Let FN be the >> > collection of all finite natural numbers. You say that >> > FN is finite. You say that that means that its size is >> > equal to some finite natural number. >> >> He never said that. He said "Some finite, indeterminate >> number." He didn't say "Some finite, >> indeterminate natural number." But even if he did, >> mathematicians have their own meaning of words >> and therefore his natural numbers might be different than >> mathematicians. > > But TO insists that OUR natural numbers have to follow HIS rules, > despite the fact that his rules contradict our rules on many issues. Then why argue with him. Tell him you use different rules and uncommon meanings of words and be done with it. >> >> > So call that number >> > L. If L is finite, then it must be an element of FN, >> > because FN is the collection of *all* finite natural >> > numbers. But that means that FN contains at least L+1 >> > elements: 0, 1, 2, ..., L. That contradicts the claim >> > that FN contains exactly L elements. >> >> Too bad he didn't imply that stuff. >> >> > Your theory is self-contradictory. Not that *you* would >> > ever notice the contradiction, because you are just making >> > things up as you go. You are just playing, not caring whether >> > what you're saying makes sense or not. >> >> I think you are the one that is trying to put nonsense into his >> post. > > No, just the one pointing it out! It was already there. There is a good > deal of nonsense n all of TO's attempts to reformulate mathematics in > his own image. He's using common word meanings. You are using (admittedly by mathematicians) uncommon word meanings.
From: Poker Joker on 28 Jul 2005 23:05 "Virgil" <ITSnetNOTcom#virgil(a)COMCAST.com> wrote in message news:ITSnetNOTcom%23virgil-3BF47C.00514828072005(a)comcast.dca.giganews.com... > In article <MPG.1d51c8215386c4f2989fd9(a)newsstand.cit.cornell.edu>, > Tony Orlow (aeo6) <aeo6(a)cornell.edu> wrote: > >> Daryl McCullough said: >> > Tony Orlow (aeo6) wrote: >> > >> > >Robert Low said: >> > > >> > >> OK, so how many elements are there in the set of all finite >> > >> natural numbers? >> > >> >> > >Some finite, indeterminate number. You tell me the largest finite >> > >number, and that's the set size. >> > >> > So you really think that there is some number n such that n is >> > finite, but if you add 1 you get an infinite number? >> (sigh) This is the last time I answer this question >> NOOOOOOOOOOO!!!!!!!!! > > But since every natural has an immediate successor, and except for the > first. an immediate predecessor, and there are no gaps( at least if one > accepts Peano), the only way of getting from finite to infinite is by > adding 1 to some finite natural to get an infinite natural. > >> > Maybe it's 7? Maybe 7 is the largest finite number, and 8 is >> > actually infinite? >> Don't be stupid. > He is just trying to come down to your level, TO. >> > >> > In fact, a set is finite if and only if the number of elements is >> > equal to a natural number. There is no largest natural number, and >> > there is no largest finite set. The collection of all finite >> > natural numbers is an infinite set. > >> The set of all finite numbers up to a given number has that number in >> it, which is also the set size. Any subset of N has a size that is in >> N. > > What member of N is the size of N? How about the size of N\{1}? The size > of the set of even naturals or the size of the set of odd naturals? > For the standard theory these all have trivially easy answers, and none > of the sizes are members of N. For TO's theory it depends on how his > medicatins are affecting him that day. What member of N is the color of N? How about the color of N\{1}? The color of the set of even naturals or the color of the set of odd naturals?
From: stephen on 29 Jul 2005 00:07 In sci.math malbrain(a)yahoo.com wrote: > Dik T. Winter wrote: >> In article <1122567294.560463.170070(a)g49g2000cwa.googlegroups.com> malbrain(a)yahoo.com writes: >> > Dik T. Winter wrote: >> ... >> > > > Well, the OBVIOUS answer to your question is, "I'm talking about C" >> > > > However, I'm not that vulgar. I tend to translate discussions into C >> > > > because I find it to be more universally understood than java. karl m >> > > >> > > So what? When someone talks about java with "unbounded" standard types, >> > > what is the point stating that C does not have "unbounded" standard types? >> > >> > How is the length of an integer determined by a java program running on >> > the virtual-java-machine? karl m >> >> Yes, what are you trying to tell? I think you would be better off when you >> get back on your chair. > Sorry, but I submitted in my position to seniority. I'll try my best > to cover my new role. > If we can get the program to determine the length of the standard > integer type we can map to the C INT_MAX declaration during execution. > karl m The discussion is about unbounded integers. They have no set length. The grow as needed, like strings. Is there a STRING_MAX declaration in C? Why not? Stephen
From: malbrain on 29 Jul 2005 01:12
stephen(a)nomail.com wrote: > In sci.math malbrain(a)yahoo.com wrote: > > Dik T. Winter wrote: > >> In article <1122567294.560463.170070(a)g49g2000cwa.googlegroups.com> malbrain(a)yahoo.com writes: > >> > Dik T. Winter wrote: > >> ... > >> > > > Well, the OBVIOUS answer to your question is, "I'm talking about C" > >> > > > However, I'm not that vulgar. I tend to translate discussions into C > >> > > > because I find it to be more universally understood than java. karl m > >> > > > >> > > So what? When someone talks about java with "unbounded" standard types, > >> > > what is the point stating that C does not have "unbounded" standard types? > >> > > >> > How is the length of an integer determined by a java program running on > >> > the virtual-java-machine? karl m > >> > >> Yes, what are you trying to tell? I think you would be better off when you > >> get back on your chair. > > > Sorry, but I submitted in my position to seniority. I'll try my best > > to cover my new role. > > > If we can get the program to determine the length of the standard > > integer type we can map to the C INT_MAX declaration during execution. > > karl m > > The discussion is about unbounded integers. They have > no set length. The grow as needed, like strings. > Is there a STRING_MAX declaration in C? Why not? Because the OPERATING SYSTEM provides enough VIRTUAL BACKING to equate STRING_MAX with INT_MAX. Non-hosted implementations are another story. karl m |