Re: Another stab at Cantor

In article <1158699227.198536.286480@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
georgie <geo_cant@xxxxxxxxx> wrote:
Arturo Magidin wrote:

Do you know what a red herring is?

Its something you would probably try, to avoid the real issue.

Very droll, Georgie. You're still being an ignoramus, though.

...
He then asserted that after doing this an infinitely
countable number of times, he would obtain a list. ->That<- assertion
is false. What he "ends up" with in the limiting case is a
"pseudo-list" (I'm making up the term right now, only for the purposes
of this paragraph)

I noticed that about you. You "make things up" as we go.

Oh, doubly droll. No wonder you are such an ignoramus.


You can't seem to accept that and have resorted to personal attacks.

Oh, I can accept perfectly well that you have failed to understand the
rebuttals. I have chosen to express my contempt for you in the form of
personal attacks. This has nothing to do with denial, but merely with
contempt.

That seems to be a character flaw that you have.

Perhaps. It is nonetheless a reflection of just how absurdly ignorant
you are.



The original poster describes a process whereby, if you have a list,
you produce a new string, pre-append it, and obtain a new
list. Lather, Rinse, Repeat.

The original poster then talks about continuing this process via the
"totality of all possible steps of this procedure." The procedure can
only be applied so long as you have a list. This can certainly be done
at each natural-numbered step. If you take the union of these steps,

Taking the union was never discussed or implied.

"Jane, you ignorant twit."

That is what, in this situation, "the limiting case" is.

You have a nested collection of ordered sets; the limiting case is
obtained by taking the union of the sets. If you didn't know that,
well, that would hardly be a suprise.


what you end up with is an ORDERED set which, AS GIVEN, is not a list;
among other reasons because each term has an infinite number of
predecessors. At this stage, the "procedure" cannot be applied, so the
process STOPS.

So we are done with ->that<- process.

If we aren't done with all possible steps, we better go back, because
that's what the OP said.

We are done will ALL steps that are possible FOLLOWING THE OP'S
INSTRUCTIONS. If you are trying to Re-write those instructions to
change his procedures, then stop being coy about it and come right out
and say so. But the OP gave a very specific procedure that does not
exhaust everything Georgie can think of; it merely exhausts a
particular process, which results in exactly the set that I have been
describing.

At this stage, it was asserted the resulting (ordered) set contains
all possible strings. That is false. While the set, ordered as given,
is not a list, it can nonetheless be REORDERED

That reordering step is a possible step.

Only if you purposely misinterpret and/or rewrite what the OP
stated. The original poster gave a VERY SPECIFIC procedure, and that
procedure DOES NOT include the ability to reorder what is given. That
procedure can only take a GIVEN list, ->AS GIVEN<-, produce its
diagonal string with respect to the GIVEN order, and return the
ordered set you obtain by taking the list AS GIVEN with the diagonal
string preappended as first term.

The process does not allow you to reorder the given list before
applying the diagonal process. As such, what I described (taking a set
which is not given as an ordered list, reordering it to make it into a
list, and then applying the diagonal process), while "possible" in the
sense of "it can be done", it is not "possible within the confines of
the procedure described by the original poster." As such, this is NOT
included in the OPs discussion.

It *MUST* be in the set of
all possible steps.

It is the set of all possible STEPS FOLLOWING THE GIVEN
INSTRUCTIONS. You are trying to change the given instructions. As
such, you are guilty of at best equivocation, and quite probably willful
confusion.

so that the result
->IS<- a list, and we can easily produce strings not on THAT list, and
therefore not in the original (ordered) set.

Except for the fact that it can't be.

Except for the fact that you are willfully equivocating on "possible
steps". What I described is not "possible within the confines of the
algorithm provided" and therefore is not contemplated in the original
construction.

I think that what is sticking in your craw is that you somehow decided
that the original poster meant to CONTINUE applying the process
anytime he could take the collection of everything he had produced
thus far and somehow turn it into a list.

I think you ignored that all possible steps means all of them,

And here is your confusion/idiocy/lie.

The procedure was explicitly described. The instructions where to
continue applying THAT PROCEDURE when possible. The instructions where
not "continue obtaining diagonal numbers any which way as long as
possible", which is what you attempt to cast it as.

not all
of them except the ones Arturo Magidin might want to describe.

You are confused. The "possible steps" described in the OP MUST follow
the given instructions, not "all the ones that Georgie Boy attempts to pull
out of his anal orifice."

But that is NOT what he said.

Even if what he said or meant was that the sky is blue, the set of all
possible steps includes steps you describe in all your posts you will
ever write or even think about.

He did not ask for "all possible ways to add diagonal terms",
moron. He asked that HIS PROCEDURE be repeated for as long as
possible. HIS PROCEDURE, not "any old procedure you can think of,
write of, or that Georgie Boy thinks are meant".


Even if he didn't have the insight to
mean to include those, we can assume he did

No, we cannot. My argument addresses WHAT HE WROTE, not what Georgie
boy decides was what he should have written.


and your argument
about reordering and such is meaningless.

My argument addresses what he wrote, not what you imagine that he
should have written. Duh.

What he gave was a specific
deterministic algorithm that does not allow you to reorder the sets
you obtain.

For the sake of argument, we could be adults and understand that
your restrictions are just avoiding the real issue.

You could be honest and recongize that your entire cogitations rely on
a dishonest equivocation, and that you are quite simply wrong. That
you are criticizing an argument I gave on the grounds that it
addresses exactly what it was written to address (to wit, what the
other poster actually wrote), and not something else. In short, that
you are being an idiot.


The OP didn't
explicitly say one way or the other

Yes, he did. You just didn't get it. He said to repeat HIS process,
and HIS process does not allow reordering.

->Of course<-, if you change the process, then there is no reason to
think that the argument given will also apply to the different
process.

so lets forget about the trivial
cases. His set of "all possible steps" includes all steps.

No, it did not. If you want to change it to mean that, then write it
out exactly and precisely, just like he did. He gave a precise
description, which you are misrepresenting by equivocation.

Then again, your character flaw may not let you be an adult. I'm
not sure.

I see you are still a wife-beater.

[...]

"If Arturo Magidin's step is a step then it is one of all possible
steps." is true.

No, it is false. You are putting far more into the procedure than the
original poster provided. And then you are claiming that the proof
presented is insufficient because it fails to address something which
was not put into the original procedure. Well, DUH.

You aren't thoroughly considering the OP.

I am thoroughly considering what the oriiginal poster wrote. I did
not, nor did I intend to, consider everything that anybody could
possibly decide to make by modifying what the original poster
provided.

He, at least, was quite specific and explicit. I addressed the
explicit, and specific, procedure he provided. You want to invent a
new one, or pull one out of your ass? Be my guest.

What I described is not a "possible step" in the original poster's
algorithm; it takes place AFTER the original poster is done with his
algorithm, which can only be applied omega times. What I described
"takes place" at step "omega + 1", which is incompatible with the
original poster's description.

What a joke.

No. It's a fact. If you cannot wrap your brain around it, well, that's
your problem.

Suppose he was thinking of your step when he said
"all possible steps".

I don't have to suppose anything. His words spoke for themselves, and
his works only allow to consider a very specific operation which does
NOT include the process I described.

It really isn't much of a stretch to think "all
possible steps" means all of them.

He said to apply HIS process, as described.

ANY stretch at all, no matter how minor, departs from his
instructions. As such, an argument designed to address HIS
instructions need not apply to anything other than HIS PRECISE, EXACT,
instructions.

You want to change the instructions because you think you can do
better? Fine. Change them, and provide your own explicit instructions,
we will deal with them then.

If you mean "start with a list, and then take all possible diagonal
strings that you can produce from any list that you can produce from
any set that includes the original list and any previously produced
strings, via any method whatosever", then say so. The result will not
be the set the original poster produced by ->his<- instructions, and
my argument will not apply. But then, my argument was not ->meant<- to
apply to that set. That set is uncountable.

Did he really need to anticipate your
argument and say "all possible steps and Arturo Magidin's steps that
wouldn't be included in the set of all steps because Arturo Magidin's
steps
are special"?

He did not need to anticipate ANYTHING. He specified EXACTLY what
steps were allowed; his "step" takes a LIST of binary strings, and
returns a LIST of binary strings. Namely, given a LIST of binary
strings, produce the diagonal string, preappend it to the given list,
and return the result. That is what he SAID. When he said repeat, it
must be understood to mean repeat ->THAT PROCESS<-. Not some other
process. Not "any" process that georgie boy decides to try. Not any
process ->I<- decide to try. ->THAT PROCESS<-, and that process
alone. If he meant something else, he should have written something
else. If YOU want to mean something else, then write something
else.

If you entire problem is that the argument designed to handle EXACTLY
WHAT WAS WRITTEN does not handly your own pet process, that's just
because you are trying to use a hammer to unscrew a phillips head.

[...]


--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
======================================================================

Arturo Magidin
magidin-at-member-ams-org

.