Re: Cantor's circular "proof" that evens = integers



BECAUSE this is the kind of thing that is done
OFTEN in MATH, there is, in MATH, a NAME
for this: IT'S CALLED A FUNCTION.
And you don't just "use parallel" whatever:
YOU *DEFINE* a FUNCTION. And you really
do HAVE to DEFINE it. You have to articulate,
clarify, and describe, CLEARLY AND IN ADVANCE,
the class of things in the DOMAIN of your function --
you have to tell what ONE side of the correspondence
is. THEN, for EVERYthing in that class, you have to
articulate, clarify, and describe, just WHAT the
"corresponding" thing (or, in this case, "label") is.

Anybody who was actually competent to be discussing
this would have, at this point, stated the domain of a
function and defined one. Instead,
On May 18, 5:38 am, Phil <toob-head...@xxxxxxxxxxxxx> wrote:
Oh really? So tell me, what is the number of the point
that corresponds to "1/2?"

*I* don't have to tell YOU ANYthing, Phool!
YOU HAVE TO TELL *US* the domain of YOUR function!
You still have not done that, because (as usual) the only thing
preventing you from being a fucking idiot is that you are too
damn stupid to get laid.
1/2 is a rational number. Are you saying that the domain of
your function is the rational numbers between 0 and 1?
If so, does the domain include 0 and 1? Does it include all
the numbers or only the halfway points? Does it include reals
or just rationals?? YOU HAVE TO SAY what YOUR domain
is before ANYthing can proceed!

How many points preceded that point?

That depends on HOW YOU defined THE DOMAIN of YOUR
function! SINCE YOU HAVEN'T YET stated a domain, nothing
else gets to happen.

Get a clue, we DEFINE a segment as being a "unit length"

NO, YOU DON'T. FIRST, You define THE DOMAIN of
your function.

which CORRESPONDS, in length,

NO, you DON'T do that, because BEFORE you could do
that, you would have to define LENGTH.
You haven't done that yet either. WE WILL get to that.
But first, you have to finish defining your "correspondence"
between "points" and numbers. And before you can do that,
YOU HAVE to define the domain of your function.

Functions can be described in terms of what they do,
or what class they belong to.

Oh, shut up. We have been talking about ZFC all day.
If that is the axiom-system you are going to use, then
a function is a set of ordered pairs and you have to define
the set. If that is NOT the axiom-system you are going to
use then YOU HAVE TO STATE *YOUR* axioms!
YOU *DON'T* get to say "I''m defining it in terms of what it
does". THIS IS *MATH*! NOTHING EVER *DOES*
anything! We DON'T do TIME and we DON'T do VERBS
(unless they are just predicates)! Things just *ARE* either
true or false, or in this or that relation to each other (and the
favorite binary relations are equality, and, if we are still in
ZFC, set-membership).


If the number of points in the segment is defined as being w,

Well, IS IT OR ISN'T IT??
Don't you have to define "segment" FIRST?
IF you define it properly, won't we BOTH THEN be able to
PROVE how many points it has in it??
In the real physical space to which you are alleging this
correpsonds, there are in fact a GREAT many MORE than
w points. But there are only w halfway-points. I repeat,
YOU have to state the domain of your function.


then this "function" is y = wx,

Oh, shut up.
If you are going to say that then YOU HAVE TO DEFINE
what MULTIPLYING by w MIGHT MEAN!
YOU DON'T KNOW!

but that doesn't mean we are forbidden from DESCRIBING
what this function is or does!

It's far worse than that: YOU HAVE SIMPLY *FAILED*
to describe this function or what it does. The turd you have
just excreted DOES NOT CONSTITUTE a description of
this function (WHAT function?!?!? YOU HAVE NOT defined
ANY function here! YOU DON'T KNOW what a FUNCTION is!)

By DEFINING

Oh, shut up. You don't know what a definition is either.

an infinite set of points as (1) having a first point,

Dip***: "infinite", "set" and "first" are ALREADY IN THE
DICTIONARY. The set of negative (integer) powers of 2,
ordered IN THE USUAL WAY, *is* an infinite set (of
rational numbers --
{...,1/1024,1/512,1/256,1/128,1/64, 1/32,1/16,1/8, 1/4,1/2}
and it DOES NOT HAVE a first element (though it does
have a last one).
YOU CANNOT define "infinite" to include "having a first point".


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