An uncountable countable set
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From: Lester Zick on 29 Oct 2006 14:08 On Sat, 28 Oct 2006 14:52:47 -0400, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On 27 Oct 2006 11:38:10 -0700, imaginatorium(a)despammed.com wrote: >> >>> David Marcus wrote: >>>> Lester Zick wrote: >>>>> On Fri, 27 Oct 2006 16:30:04 +0000 (UTC), stephen(a)nomail.com wrote: >>>>>> A very simple example is that there exists a smallest positive >>>>>> non-zero integer, but there does not exist a smallest positive >>>>>> non-zero real. >>>>> So non zero integers are not real? >>>> That's a pretty impressive leap of illogic. >>> Gosh, you obviously haven't seen Lester when he's in full swing. (Have >>> _you_ searched sci.math for "Zick transcendental"?) >> >> Hell, Brian, on some of my better days I can even prove the pope's >> catholic. >> >> ~v~~ > >That must be a proof by contradiction. It's proof by transcendental analysis, Tony. > It doesn't involve a largest >finite, does it? ;) Not sure, Tony: this isn't one of my better days. ~v~~
From: Lester Zick on 29 Oct 2006 14:25 On 28 Oct 2006 12:54:51 -0700, "Randy Poe" <poespam-trap(a)yahoo.com> wrote: > >Lester Zick wrote: >> On Fri, 27 Oct 2006 14:23:58 -0400, David Marcus >> <DavidMarcus(a)alumdotmit.edu> wrote: >> >> >Lester Zick wrote: >> >> On Fri, 27 Oct 2006 16:30:04 +0000 (UTC), stephen(a)nomail.com wrote: >> >> >A very simple example is that there exists a smallest positive >> >> >non-zero integer, but there does not exist a smallest positive >> >> >non-zero real. >> >> >> >> So non zero integers are not real? >> > >> >That's a pretty impressive leap of illogic. >> >> "Smallest integer" versus "no smallest real"? Seems pretty clear cut. > >You must be joking. I can't believe even you can be this dense. Oh I dunno. I can be pretty dense. Just not as dense as you, Randy, but that's nothing new. >Is 1 the smallest positive non-zero integer? Yes. > >Is it the smallest positive non-zero real? No. 1/10 is smaller. >Ah well, then is 1/10 the smallest positive non-zero real? No, >1/100 is smaller. Is that the smallest? No, 1/1000 is smaller. > >Does that second sequence have an end? Can I eventually >find a smallest positive non-zero real? > >How about the first? Is there something smaller than 1 which >is a positive non-zero integer? See the problem here, Randy, is that you're explaining an issue I didn't raise then pretending you're addressing the issue I raised. I don't doubt there is no smallest real except in the case of integers. But that is not what was said originally. What was said is that there is a least integer but no least real. Now these strike me as mutually exclusive predicates. But then who am I to analyze mathematical predicates in logical terms especially when there are self righteous neomathematikers around who prefer to specialize in name calling rather than keep their arguments straight in reply to simple queries. ~v~~
From: Lester Zick on 29 Oct 2006 14:26 On Sat, 28 Oct 2006 16:04:22 -0400, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >Randy Poe wrote: >> Lester Zick wrote: >> > On Fri, 27 Oct 2006 14:23:58 -0400, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >> > >Lester Zick wrote: >> > >> On Fri, 27 Oct 2006 16:30:04 +0000 (UTC), stephen(a)nomail.com wrote: >> > >> >A very simple example is that there exists a smallest positive >> > >> >non-zero integer, but there does not exist a smallest positive >> > >> >non-zero real. >> > >> >> > >> So non zero integers are not real? >> > > >> > >That's a pretty impressive leap of illogic. >> > >> > "Smallest integer" versus "no smallest real"? Seems pretty clear cut. >> >> You must be joking. I can't believe even you can be this dense. > >You think Lester is trolling? If so I've certainly already caught the legal limit of trolls. >> Is 1 the smallest positive non-zero integer? Yes. >> >> Is it the smallest positive non-zero real? No. 1/10 is smaller. >> Ah well, then is 1/10 the smallest positive non-zero real? No, >> 1/100 is smaller. Is that the smallest? No, 1/1000 is smaller. >> >> Does that second sequence have an end? Can I eventually >> find a smallest positive non-zero real? >> >> How about the first? Is there something smaller than 1 which >> is a positive non-zero integer? ~v~~
From: Lester Zick on 29 Oct 2006 14:28 On 28 Oct 2006 13:07:02 -0700, imaginatorium(a)despammed.com wrote: > >Randy Poe wrote: >> Lester Zick wrote: >> > On Fri, 27 Oct 2006 14:23:58 -0400, David Marcus >> > <DavidMarcus(a)alumdotmit.edu> wrote: >> > >> > >Lester Zick wrote: >> > >> On Fri, 27 Oct 2006 16:30:04 +0000 (UTC), stephen(a)nomail.com wrote: >> > >> >A very simple example is that there exists a smallest positive >> > >> >non-zero integer, but there does not exist a smallest positive >> > >> >non-zero real. >> > >> >> > >> So non zero integers are not real? >> > > >> > >That's a pretty impressive leap of illogic. >> > >> > "Smallest integer" versus "no smallest real"? Seems pretty clear cut. >> >> You must be joking. I can't believe even you can be this dense. > >Hmm, you must be new to Usenet? (Lester has just informed me - no idea >why, since I didn't ask him - that he considers himself an original >thinker.) Just wanted to round off your otherwise unoriginal education, Brian. >> Is 1 the smallest positive non-zero integer? Yes. >> >> Is it the smallest positive non-zero real? No. 1/10 is smaller. >> Ah well, then is 1/10 the smallest positive non-zero real? No, >> 1/100 is smaller. Is that the smallest? No, 1/1000 is smaller. >> >> Does that second sequence have an end? Can I eventually >> find a smallest positive non-zero real? >> >> How about the first? Is there something smaller than 1 which >> is a positive non-zero integer? > >You also must be unaware that this is a poetry thread... Haiku, anyone? ~v~~
From: Lester Zick on 29 Oct 2006 14:30
On Sat, 28 Oct 2006 16:55:41 -0400, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >Virgil wrote: >> In article <45435a9c(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: >> > David Marcus wrote: >> > > Tony Orlow wrote: >> > >> MoeBlee wrote: >> > >>> Tony Orlow wrote: >> > >>>> Eat me. Do you maintain that the two theories are compatible with each >> > >>>> other? Is there, and also not, a smallest infinity. >> > >>> They're not in conflict, becuase 'smallest infinite' means something >> > >>> DIFFERENT in the different contexts. How many times will I say that >> > >>> while you STILL refuse to hear it? >> > >> So, either smallest has two meanings, or infinite has tow meanings, or >> > >> both. Would you like to elucidate the matter by enumerating the various >> > >> definitions of "small" and "infinite"? A table might be nice... >> > > >> > > As many have said, "infinite" has many meanings. I'm afraid it isn't >> > > practical to produce a table. >> > >> > How about a list? ;) >> >> As lista are merely function having N as domain, and functions can often >> be given by formulae, it is easy to produce some lists. >> >> For example, f:N -> R: n |-> n, is a simple list. > >Tony wants a list of all the meanings of the word "infinite" in >mathematics. Good thing he doesn't want even one mathematical definition of infinity. ~v~~ |