An uncountable countable set
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From: Virgil on 1 Oct 2006 19:51 In article <45203919(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > > Since ordinals are, by definition, well ordered, they cannot contain any > > endlessly decreasing sequences, which TO's models require. > > Neither can the reals. How about the set of negative integers? How is that not an endlessly decreasing sequence of reals?
From: Virgil on 1 Oct 2006 19:52 In article <452039fb$1(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <4520254e(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > > > >> In the binary number circle, "100...000" is both positive and > >> negative infinity. > > > > What about "100...0001"? > > That is the actual greatest negative integer Self-contradictory.
From: Virgil on 1 Oct 2006 19:56 In article <45203f37(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <452032b9(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > >> Virgil wrote: > >>> In article <45201554(a)news2.lightlink.com>, > >>> Tony Orlow <tony(a)lightlink.com> wrote: > >>>> Virgil wrote: > >>>>> A set is a container, and is not one of the objects that it contains. > >>>> It is nothing more or less than its contents. > >>> It is determined uniquely and entirely by its contents, as stated in the > >>> axiom of extentionality. > >> So we agree. There is nothing besides the members. > > > > To say that it is completely determined by its members is not to say > > that it "is nothing besides its members". If it were nothing besides its > > members we cold not give it a name as a thing of its own. > > So, it is completely determined by its members, but that's not all there > is to its determination. Uh huh. TO tries so hard not to understand that the he almost always succeeds in not understanding, as here.
From: Virgil on 1 Oct 2006 20:04 In article <45203fff(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <45202ef3(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > >> If one changes a rule in a specific way, it will have a specific > >> consequence. > > But not necessarily relevant to what would occur without the change. > > You mean the specifics of the change have no relation to the changes of > the specifics? That may be what TO says but is not at all what I said. I said that the rules determine the outcomes possible, and different rules need not produce the same outcomes. Thus only the original rules are relevant in delimiting the possible outcomes that can follow from those original rules. > I rather doubt anyone in their right mind agrees. As TO does not seem to have any meeting of minds with anyone in his or her right mind, how would TO be able to tell what such a person would agree to?
From: Tony Orlow on 1 Oct 2006 20:34
MoeBlee wrote: > mueckenh(a)rz.fh-augsburg.de wrote: >> This is an extremely good example that shows that set theory is at >> least for physics and, more generally, for any science, completely >> meaningless. > > Except that set theory axiomatizes the portions of standard mathematics > used by physics and the sciences. > > You say that set theory is meaningless as you work on a computer that > depends on the advent of technology hastened from the theoretical > contexts of mathematical logic and set theory. > > MoeBlee > Transfinitology is an unsound extension of what "works" in the finite case. |