Re: An uncountable countable set

On 26 Oct 2006 13:38:33 -0700, "MoeBlee" <jazzmobe@xxxxxxxxxxx> wrote:

Lester Zick wrote:
On 25 Oct 2006 17:17:42 -0700, "MoeBlee" <jazzmobe@xxxxxxxxxxx> wrote:

Lester Zick wrote:
At least to
me the "well" in "well ordered" is redundant. If a set is ordered it
is "well ordered" and if not it's not ordered. Of course as you note I
haven't studied the arcana of conceptual techniques in standard set
analysis so I may be mistaken but that's how it appears.

You are mistaken. And it is not an arcane point. Look, such terms as
'well ordered' are specific in mathematics and are not proposed to
serve in the same role as such everyday notions as 'ordered'.

So they're not predicates after all? Curiouser and curiouser.

Who said they're not predicates?

Oh so they are predicates and yet don't serve in the same role as
predicates in everyday notions. I'm so confused, Moe.

And where exactly do transcendentals fit in this so called "linear"
ordering of the reals?

Between other real numbers, as do all real numbers.

Yeah well that's really curious, Moe, since curves don't fall on
straight lines except when they actually go through the looking glass
and sometimes not even then.

There is no consistent theory that includes expression of arithmetic of
the natural numbers that can provide for an algorithm to determine the
truth of sentences in the language of the theory. It would be nice if
this weren't the case, but, alas, it is.

And you know this how exactly?

By having read a proof.

A proof that there can be "no consistent theory . . .". Truly
fascinating. Do tell us more about this proof.

Meanwhile, at least we can provide theories of which we DO have
algorithms to determine whether something is or is not a proof from the
axioms of the theory.

We can certainly assume the algorithms okay. And we can assume the
axioms. And we can certainly assume algorithms are produced from the
axioms we assume.

No, not from the axioms of the object theory.

Oh god. I just knew it. Another axiom of other "theories" to prove
"theories" which can't be proven at all except by resort to childish
assumptions of truth. Is there no end to these fucking extraneous
axioms?

Jeez, Moe, gimme a break already. So if I'd said 1, 2, 3 . . .infinity
in that post you would have been impressed whereas now you're busting
my chops because I only showed such and such is demonstrably true and
all things mathematical and scientific have to be consistent with it
in order to be true but you're perfectly content to go on assuming the
truth of whatever you claim instead with no demonstrable foundation of
truth whatsoever? Gimme a fucking break, slick.

I just asked what mathematics you endorse.

Arithmetic: 1, 2, 3 . . . The calculus: disintegration and integration
of definite integrals. Infinity as the number of infinitesimals. Not
grading on the curve. 100% grading system instead of the 4.0. I'm
still working on the rest. You'll just have to be patient. Rome wasn't
built in a day and mathematics wasn't disintegrated in a day.

I know you endorse what you
consider to have demonstrated to be true about all things mathematical
and scientific. But I had also asked as to what specific mathematics
you endorse, as it is writtten anywhere, in books, articles, on the
Internet, by anyone, including you.

See above.

If you don't want to refer me to such mathematics, then fine. But then
you are just silly when you say things about your not knowing what
mathematics I endorse, since I have too many times already mentioned
some of the textbooks I study.

Yeah, sure, Moe. You spend too much time studying and not enough time
thinking for yourself.

~v~~
.

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