PROOF INFINITY DOES NOT EXIST! Not even ONE type [Logic]

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From: Marshall on 11 Jul 2010 01:50

On Jul 10, 10:38 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote:
> K_h wrote:
> > "Nam Nguyen" <namducngu...(a)shaw.ca> wrote in message
> >news:MTSZn.2663$Bh2.125(a)newsfe04.iad...
> >> K_h wrote:
> >>> Mathematical truth exists.
> >> Sure. In your mind for example!
>
> > And also outside of the human mind.
>
> Did you mean _physically outside of human mind_ ? That's very bizarre to say
> of mathematical abstractions that human thinks of. No?
>
>
>
> >>> The equation 10+20=30 is an absolute truth and that truth does exist.
> >> Again, in your mind perhaps. Others working in modulo arithmetic
> >> may state 10+20=0 is absolutely true, just as you stated "10+20=30
> >> is an absolute truth". What's the difference anyway?
>
> > If you don't believe that 10+20=30 is true in regular arithmetic then there's not
> > much point in arguing it. Obviously I was not referring to modulo arithmetic.
>
> I didn't say I don't believe such in regular arithmetic. But if you have to
> refer to regular arithmetic then that isn't "an absolute truth" as you had
> incorrectly claimed! An absolute mathematical truth is a statement which is
> just true _independent of any context_ that you're referring to. And there
> isn't such an absolute truth.
>
>
>
> >>> So you have existential doubts about the truth of 4+5=9?
> >> People have no doubt that 4+5=9 is false in some modulo arithmetic.
>
> > So we agree that there are absolute truths in both regular and modulo arithmetic.
>
> No, I didn't agree to that. A truth that requires a context for it to be true
> isn't an absolute truth. And in any rate it's not "outside of the human mind"
> as you incorrectly stated above.
>
> --
> ----------------------------------------------------
> There is no remainder in the mathematics of infinity.
>
> NYOGEN SENZAKI
> ----------------------------------------------------

Just an FYI for K_h, Nam is a complete buffoon and you
should not feel the least bit compelled to respond to his
nonsense. As I'm sure is already clear from the above.

Marshall

From: Transfer Principle on 11 Jul 2010 02:03

On Jul 9, 6:22 am, Wolf K <weki...(a)sympatico.ca> wrote:
> On 08/07/2010 23:04, |-|ercules wrote:
> > Transfinite theory is just oo+1 > oo. And it works on EVERY example,
> > you may choose another animal if 2 elephants is Aleph_2 or some BS.
> Dear Herc: You have demonstrated the classic traits of a crank:

Here we go again with the five-letter insults! But let's take a look
at why Wolf K. chose that word to describe Herc:

> a) announce a proof that some widely accepted
> principle/theorem/insight/etc that violates your notions of reality is
> wrong, using arguments rife with unstated assumptions, vague
> definitions, and shifting meanings

First of all, just because a principle is "widely accepted," it
doesn't
mean that Herc has to accept it. After all, "widely accepted" isn't
the same as "unanimous accepted." Finitism is a respectable
mathematical position, even though it's not the majority position. And
there are many other mathematical positions, such as intuitionism
and constructivism, that aren't "widely accepted," yet there are still
such mathematicians.

Furthermore, about "violating [one's] notions of reality," I point out
that set theorists reject axioms that violate their notions of reality
all the time. For example, they reject V=L because it's too
restrictive and say that it's not "really true." If set theorist can
reject "V=L," then Herc can reject the Axiom of Infinity.

Thus, I interpret a) as saying that Wolf K. calls posters "cranks"
when they violate _his_ (i.e., Wolf K.'s) notion of reality.

> b) express your proof in technical terminology that you do not understand

Now b) makes the common assumption that if one doesn't
accept a theory, then one must not understand it. Yet surely
it's possible for a finitist to understand infinitary terminology
without accepting it, just as it's possible for an atheist or
Muslim to understand the Bible without accepting it.

> c) attempt to refute the corrections and clarifications politely offered
> by people who understand the field

But what constitutes a "correction" is subject to opinion -- a
classical analyst might consider telling a finitist about infinity
to be "correcting" them, just as a Muslim might consider
telling an atheist or Christian about the Quran to be "correcting:
them, too. It's only natural that a finitist would refute these
so-called "corrections," just as it's natural for the adherents of
a religion to resist conversion to another religion.

> d) resort to ad hominem arguments;
> e) descend into personal insult.

Posters on both sides of the debate do both all the time. So
according to d) and e), nearly every poster is a "crank."

Thus, I disagree with all five justifications that Wolf K. gives for
calling Herc a "crank."

From: Nam Nguyen on 11 Jul 2010 02:03

Marshall wrote:
> On Jul 10, 10:38 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote:
>> K_h wrote:
>>> "Nam Nguyen" <namducngu...(a)shaw.ca> wrote in message
>>> news:MTSZn.2663$Bh2.125(a)newsfe04.iad...
>>>> K_h wrote:
>>>>> Mathematical truth exists.
>>>> Sure. In your mind for example!
>>> And also outside of the human mind.
>> Did you mean _physically outside of human mind_ ? That's very bizarre to say
>> of mathematical abstractions that human thinks of. No?
>>
>
> Just an FYI for K_h, Nam is a complete buffoon and you
> should not feel the least bit compelled to respond to his
> nonsense. As I'm sure is already clear from the above.

You must have agreed with K_h that "Mathematical truth exists ...
outside of the human mind", because you don't seem to be able
to recognize and gave a technical critique such a nonsense, right?

Of course _that's all Marshall could utter in technical matters_
in the foundation: _idiotic babbling and attacks_.

--
----------------------------------------------------
There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI
----------------------------------------------------

From: Transfer Principle on 11 Jul 2010 02:54

On Jul 9, 6:22 am, Wolf K <weki...(a)sympatico.ca> wrote:
> IOW, you stopped thinking around grade 5 or 6.

Wolf K.'s reference to grades 5-6 here is interesting, since
this is around the age that students are required to refer to
infinitary concepts.

For example, according to the Common Core Standards
for Mathematics, Grades 6-8:

6.EE Expressions and Equations
8. Write an inequality of the form x > c or x < c to represent
a constraint or a condition in a real-world or mathematical
problem. Recognize that inequalities of the form x > c or
x < c have _infinitely_many_solutions_; represent solutions
of such inequalities on number line diagrams.
(emphasis mine)

7.NS The Number System
2d. Convert a rational number to a decimal using long
division; know that the decimal form of a rational number
terminates in 0s or eventually repeats.

8.EE Expressions and Equations
7a. Give examples of linear equations in one variable with
one solution, _infinitely_many_solutions_, or no solution.
(emphasis mine)

I give the (controversial, here in the U.S.) Common Core
Standards rather than my own state's as in order to avoid
leaving out the other 49 states.

But then again, this is an international audience. I see that
Wolf K. has a Canadian email address, while I know that
Herc is an Australian. I believe that Canadians enter the
sixth grade at around the same age that Americans do, but I
don't know about Australia's age grouping.

So Wolf K. accuses Herc of having stopped thinking since he
was 11 or 12, since this is the age at which one typically
learns about infinity. But Wolf K.'s comment about the sixth
grade becomes ironic when we juxtapose it with another
comment that he makes in this very thread about that same
grade level:

> The dictionary records what the dictionary maker figures people mean
> when they use words. The dictionary doesn't stipulate anything, even
> though many people (still dazed by the nonsense passed off as "grammar
> in grade 6) believe that the dictionary tells you waht words "really" mean.

Aha! So Wolf K. considers dictionary definitions to be "the
nonsense passed off as 'grammar' in grade 6" in the exact
same way that Herc considers infinity to be the nonsense
passed off as mathematics in grade 6. Yet Wolf K. accuses
Herc of having stopped thinking in grade 6, since the latter
rejects "there are infinitely many numbers," which he should've
learned about back in grade 6. Then, why can't I accuse Wolf
K. of having stopped thinking in grade 6, since Wolf K. rejects
"dictionary definitions are _the_ definition," which _he_ should've
learned about back in grade 6? After all, what's good for the
goose is good for the gander!

But I don't believe that Wolf stopped thinking in grade 6 just
because he disagrees with his sixth grade teacher. Instead, I
believe that Wolf is a descriptivist -- i.e., someone who believes
that it's how people use a word in real life that determines what
_the_ definition of a word is, rather than what some dictionary
_prescribes_ the definition to be.

Likewise, Herc didn't stop thinking when he was 11 or 12 just
because he disagrees with his teacher. Instead, I believe that
Herc is a finitist -- i.e., someone who believes that the only sets
that exist are finite -- since real life deals with finite objects --
rather than the sets that some axioms _prescribe_ to exist.

Rather than stopped thinking, Wolf _started_ thinking that what
he learned is wrong and became a descriptivist. Similarly,
rather than stopped thinking, Herc _started_ thinking that what
he learned is wrong and became a finitist.

From: Curt Welch on 11 Jul 2010 12:11

"K_h" <KHolmes(a)SX729.com> wrote:
> In regular arithmetic 4+5=9 is true but Curt was claiming
> that there is some tiny chance it could be wrong in regular arithmetic.
> Curt is obviously wrong there.

If you limit the scope of the measure of "truth" to "in regular arithmetic"
then you are correct, it's an absolute truth. I was not talking about "in
regular arithmetic". I was talking about "in life". I was talking about
reality vs the fairy tale stories we make up called "in regular
arithmetic". In the stories we make up, we pretend that absolute truth can
and does exist, and all of math takes place in that fairy tale land. It's
highly useful and important to do math under that belief. But what's
invalid, is to assume the lies we use to do math, actually happen (or
exist) in the real world.

I can produce language that describes a reality where pink flying elephants
with no mass exist. But no one is going to get confused about whether the
reality I am talking about actually exists in our universe or not. It's
just a story I made up by taking things that do exist in our universe, and
combining them in a way that has never been seen, and which is highly
unlikely to ever be seen in our universe. That's how the idea of absolute
truth was created as well.

But yet, somehow, many people get so engrossed in the stores we make up as
we talk the language of mathematics, they start to believe the world of
mathematics is not just a story, but that it actually exists. That it not
only exists, but that it "lives on" even after all the story tellers die
off. It is as if they believe the pink elephants exist and live on
forever, even after everyone that's heard the story has died off.

--
Curt Welch http://CurtWelch.Com/
curt(a)kcwc.com http://NewsReader.Com/