Galileo's Paradox
in [Math]
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From: MoeBlee on 11 Dec 2006 16:05 Tony Orlow wrote: > I claimed no such thing. I am saying his very reasonable approach > directly contradicts the very concept of the limit ordinals, which are > schlock, WHAT contradiction? Robinson uses classical mathematical and set theory all over the place. > and can stay in their little paradise/cave, while the rest of > the world starts to take a more reasonable and less mystical approach to > the infinite. Ordinals and cardinals are unrelated to anything worth > bothering with. You seem to want to bother with non-standard analysis and with IST. > >> Of course, he has no need for omega. It's illegitimate schlock, like I said. What are you TALKING ABOUT? Read Robinson (which means reading the actual development, not just isolated passages), why don't you, instead of ignorantly spouting about what YOU THINK he does and does not need. MoeBlee
From: Virgil on 11 Dec 2006 16:07 In article <457D7067.7030006(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/6/2006 8:02 PM, David Marcus wrote: > > Eckard Blumschein wrote: > >> I did not consider measures. Let's get concrete. Are there more naturals > >> than odd naturals? This question could easily be answered if there was a > >> measure of size. > > > > It can easily be answered once you say what you mean by "more". Why do > > you think that common English words have unambiguous mathematical > > meanings? > > More is just inappropriate as to describe something infinite. There are > not more naturals than rationals. There are not equaly many of them, > there are not less naturals than rationals. That EB chooses not to consider measures of sizes of sets which can be applied to Dedekind infinite sets does not mean that no one else is allowed to do so. Willful blindness is not a mathematically valid criticism of Cantor. The Cantor definition of cardinality, at least in ZFC or NBG, is well-defined and self-consistent, and as such is a valid measure of set size.
From: Virgil on 11 Dec 2006 16:09 In article <457D70D8.9080902(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > Can you reveal just one illusion of mine? That you know more about mathematics than the thousands upon thousands of those who have studied it much harder and longer then you have done.
From: Virgil on 11 Dec 2006 16:16 In article <457D733C.9010604(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/6/2006 8:33 PM, Virgil wrote: > > In article <4576E3FF.9090803(a)et.uni-magdeburg.de>, > > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > > > >> On 12/5/2006 11:14 PM, Virgil wrote: > >> > In article <457584A4.3000108(a)et.uni-magdeburg.de>, > >> > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > >> > > >> >> On 12/5/2006 12:16 AM, Virgil wrote: > >> >> > In article <4574755B.4070507(a)et.uni-magdeburg.de>, > >> >> > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > >> > > >> >> >> 2*oo is not larger than oo. Infinity is not a quantum but a quality. > >> >> > > >> >> > Which "infinity" is that? > >> >> > >> >> We do not need different infinities. > >> > > >> > Cantor did. And showed why with two separate proofs. > >> > >> I pointed to the 4th and only correct possibility of interpretation to DA2. > > > > That is your opinion, but not one accepted by the mathematically > > literate. > > One has to be pretty literate in order to know this well hidden option. One can be highly literate and simultaneously highly illogical. I have known highly literate poets whose mathematics skills and formal logical skills were effectively nonexistent. > > > > > > >> Do not hope for maintaining the proof concerning the power set. > > > > Do not hope to destroy what you do not understand. > > Well, I had to understand the illusions first. You do not even understand your own illusions yet , much less anyone else's. > > > > >> The reason why the power set is also uncountable is quite simpel > > > > And Cantor showed it. > > No. Cantor again merely showed by contradiction that the power set is > not countable. The reason is: Already the entity of all natural numbers > is an uncountable fiction. Not in ZFC or NBG. Since EB cannot state clearly all his assumptions, he does not have any coherent system at all, just a collection of unsorted prejudices.
From: Virgil on 11 Dec 2006 16:19
In article <457D75A0.1060201(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/6/2006 9:10 PM, Virgil wrote: > > In article <4576F816.5060809(a)et.uni-magdeburg.de>, > > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > > > >> On 12/6/2006 12:03 AM, Virgil wrote: > > > >> > DA2 does not define anything. But if they were to b e defined by a > >> > theorem, they would already be defined by what I will call DA1. > >> > >> DA1 dealt with rationals. > > > > By DA1 I was referring to Cantor's first proof of the uncountability of > > the reals, and it deals with far more than the rationals. > > ??? What paper? Do you mean Cauchy's zig-zag diagonalization? As anyone but a fool would have known I meant: http://en.wikipedia.org/wiki/Cantor%27s_first_uncountability_proof |