An uncountable countable set
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From: Tony Orlow on 16 Oct 2006 22:05 MoeBlee wrote: > Tony Orlow wrote: >> No, set theory confuses the issue with its concentration on omega. > > Oh boy, here we go again with "Set theory confuses...". Please just way > which axioms of set theory you reject and which ones you use instead. > > MoeBlee > Uh, what axioms of set theory are specifically involved in your "proof"? I don't remember a deduction from those axioms. Perhaps you could refresh my memory.
From: Tony Orlow on 16 Oct 2006 22:07 MoeBlee wrote: > P.S. > > I lost the context, but somewhere you (Orlow) posted: > > "ZF and NBG don't handle sequences or their sums, but only unordered > sets" > > Z set theory defines and proves theorems about ordered tuples, finite > and infinite sequences, and infinite summations and infinite products > and many other things like that. > > MoeBlee > Huh! But I thought sets were unordered. If the theory of infinite series is derived from set theory, how come they seem to contradict each other here? I don't recall a derivation or proof of the empty vase from the axioms of set theory.
From: Tony Orlow on 16 Oct 2006 22:10 David Marcus wrote: > MoeBlee wrote: >> Tony Orlow wrote: >>> No, set theory confuses the issue with its concentration on omega. >> Oh boy, here we go again with "Set theory confuses...". Please just way >> which axioms of set theory you reject and which ones you use instead. > > Good suggestion. But, what do you think the chance is that Tony will > actually do that? > I have done it lots of times. I've talked about infinite case induction, the Inverse Function Rule, N=S^L, and in this case specifically, that you cannot rearrange events which are stated to be in a specific order. That last one is just a general no-no. We have been over the rearranging of infinite series, which was claimed to prove their case, and its invalidity. MoeBlee can pretend we haven't discussed all that. I don't care.
From: Tony Orlow on 16 Oct 2006 22:13 stephen(a)nomail.com wrote: > David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >> MoeBlee wrote: >>> Tony Orlow wrote: >>>> No, set theory confuses the issue with its concentration on omega. >>> Oh boy, here we go again with "Set theory confuses...". Please just way >>> which axioms of set theory you reject and which ones you use instead. > >> Good suggestion. But, what do you think the chance is that Tony will >> actually do that? > > Tony has said that he does not like the axiom of infinity and > the axiom of choice. Unlike many people who object to the > axiom of infinity, Tony believes in infinite sets. He has more > infinities than most. As for the axiom of choice, does > the analysis of the balls in the vase problem use the axiom > of choice? > > Stephen Thanks, Stephen. I am wondering the same thing. How does one formally prove this from the axioms of ZFC? I believe this uses AoC, and no, I don't like it. To me, what the Axiom of Choice really should be conveying is a dimensional aspect to set, which I think is something it's used for, but I think it is abused beyond that. So, I have the same question. How is this proven from the axioms?
From: Tony Orlow on 16 Oct 2006 22:15
MoeBlee wrote: > stephen(a)nomail.com wrote: >> Tony has said that he does not like the axiom of infinity and >> the axiom of choice. Unlike many people who object to the >> axiom of infinity, Tony believes in infinite sets. > > Okay, so that leads to the second part of my message. If he rejects the > axiom of infinity (does he actually?), then how does he get the > existence of infinite sets? Of course, this is meaningless for me to > ask, since he has no theory - just jumbles of undefined and circularly > defined verbiage. > > MoeBlee > Ugh. I have given you the axioms of internal and external infinity. But, never mind. I haven't been in a state to concentrate on my axiom system for a while. So, I'll let you know... |