Galileo's Paradox
in [Math]
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From: Eckard Blumschein on 6 Dec 2006 12:09 On 12/6/2006 12:06 AM, Virgil wrote: > In article <4575B119.2050709(a)et.uni-magdeburg.de>, > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > >> On 12/4/2006 11:32 AM, Bob Kolker wrote: >> > Eckard Blumschein wrote: >> > >> >> Notice, there is not even a valid definition of a set which includes >> >> infinite sets. Cantor's definition has been declared untennable for >> >> decades. >> > >> > That is simply not so. For example the set of integers. There is is. >> >> Perhaps, you are honestly bold. Believe me that Fraenkel admitted that >> Cantor's definition is untennable. > > So Fraenkel is wrong! This time definitely not. >> The question is e.g. in case of the >> naturals whether they are considered one by one or altogether like an >> entity. While a set is usually imagined like something set for good, >> this point of view is unrealistic. > > It is essential. And since all numbers are unrealistic in that they are > only imagined, that is no handicap. Unrealistic means self-contradictory. Infinity cannot be at the same time something to approach indefinitely and something that has been reached. Tere is no end of something neverending besides within the realm of mathematical fiction. When will you comprehend this?
From: Eckard Blumschein on 6 Dec 2006 12:12 On 12/6/2006 12:08 AM, Virgil wrote: > In article <4575B16C.6050508(a)et.uni-magdeburg.de>, > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > >> On 12/4/2006 9:47 AM, Virgil wrote: >> > In article <4573D4DA.4040709(a)et.uni-magdeburg.de>, >> > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: >> > >> >> On 12/3/2006 8:22 PM, cbrown(a)cbrownsystems.com wrote: >> >> > Tony Orlow wrote: >> >> > >> >> > Well, you used the term "set" four times in your above definition of >> >> > what we mean by a "set". That's why I said "this begs the question, >> >> > what do we mean, exactly, by a set of properties?". >> >> > >> >> > There's something that we intuitively seem to think of as a "set"; but >> >> > unless such a thing is carefully defined, we end up with the >> >> > contradictions of naive set theory: >> >> > >> >> > http://en.wikipedia.org/wiki/Naive_set_theory >> >> >> >> Is it really justified to blame an allegedly insufficient definition of >> >> the term set for obvious antinomies of set theory? >> > >> > >> > As "set" and "is a member of" are primitives in axiomatic set theory, >> > any "definition" of them is outside of set theory and irrelevant to it. >> >> Yes. The problems are shifted outside. > > Nothing outside of an axiom system can be a problem inside that system. As long as one merely intends to perform sandpit-mathematics.
From: Mike Kelly on 6 Dec 2006 12:21 Bob Kolker wrote: > Mike Kelly wrote: > > > > > > By "b)" I was referring to the statement > > > > "(b) proper subsets are smaller than their supersets " > > what do you mean by "smaller"? If you mean the cardinality, what you say > is just plain wrong. The set of even integers has the same cardinality > as the set of integers, for example. > > > > > > > that was made several posts earlier in the thread. SixLetters doesn't > > see why this leads to a contradiction. I tried to explain it. > > Whatever you "explanation", if you are referring to cardinality you are > just plain wrong. > > Bob Kolker I really can't be bothered. It wasn't a statement by me. Go back and read the thread instead of being condescending. -- mike.
From: Lester Zick on 6 Dec 2006 12:26 On Wed, 6 Dec 2006 00:55:44 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >Eckard Blumschein wrote: >> On 11/29/2006 6:12 PM, stephen(a)nomail.com wrote: >> > Again, your problem is insisting that cardinality match some vague notion of 'how many' >> > that you have not defined. >> >> The basic problem is: He lacks the insight that cardinality is a >> cardinal mistake, > >Ah, mathematical argument via pun. > >> something that has proven unfounded as well as useless. > >Define "unfounded". Define "define". ~v~~
From: Lester Zick on 6 Dec 2006 12:30
On Wed, 06 Dec 2006 08:57:24 -0500, Bob Kolker <nowhere(a)nowhere.com> wrote: >Han de Bruijn wrote: > > >> >> Where w = 2 . See: > >Typo. The 'w' key is just below the '2' key. Fumble fingers. Fumble fingers or fumble mind? ~v~~ |