Infinitesimal Arithmetic

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Topic:	Science > Physics
User:	"Lester Zick"
Date:	08 May 2007 11:28:48 AM
Object:	Infinitesimal Arithmetic

Infinitesimal Arithmetic
~v~~
It's curious that for any finite r, infinitesimal i, and transfinite
I, the same people who understand I+r=I have such difficulty
understanding r+i=r.
~v~~
.

User: "Lester Zick"
Title: Re: Infinitesimal Arithmetic	28 May 2007 06:41:21 PM

On Sun, 27 May 2007 19:50:44 -0400, Tony Orlow <tony@lightlink.com>
wrote:

You have to start with some assumptions. What makes you think there is
such a thing as truth? You assume so.

Yeah, Tony, look you've already said all the rest before. You have to
start with some assumptions? You have to start with one assumption.
You demonstrate its truth. If you start with more than one assumption
you wind up using one assumption to demonstrate the truth of another.
What makes me think there is such a thing as truth? I don't. I think
there is such a thing as self contradiction which I consider false and
there is such a thing as an alternative to self contradiction which I
consider true because it is the universal tautological alternative to
what I think is false and as such the two are mechanically exhaustive
of the possibilities for truth.
If you can do better than that go right ahead. Just don't expect to
hand me a bunch of things labeled true and false and expect me to
agree with your assumptions.
~v~~
.

User: "Tony Orlow"
Title: Re: Infinitesimal Arithmetic	29 May 2007 12:16:06 PM

Lester Zick wrote:

On Sun, 27 May 2007 19:50:44 -0400, Tony Orlow <tony@lightlink.com>
wrote:

You have to start with some assumptions. What makes you think there is
such a thing as truth? You assume so.

If you only start with one assumption, it's pretty damn near impossible
to prove ANYTHING beyond that one assumption.

What makes me think there is such a thing as truth? I don't. I think
there is such a thing as self contradiction which I consider false and
there is such a thing as an alternative to self contradiction which I
consider true because it is the universal tautological alternative to
what I think is false and as such the two are mechanically exhaustive
of the possibilities for truth.

So, you agree that there are two possibilities for truth, and claim to
desires "exhaustive mechanical explanations" of truth, but refuse to
consider the binary representation of those two truth values?

If you can do better than that go right ahead. Just don't expect to
hand me a bunch of things labeled true and false and expect me to
agree with your assumptions.

~v~~

You're the one who just said, "the two are mechanically exhaustive
of the possibilities for truth". What do you intend to do with those
possibilities?
01oo
.

User: "Lester Zick"
Title: Re: Infinitesimal Arithmetic	29 May 2007 05:46:26 PM

On Tue, 29 May 2007 13:16:06 -0400, Tony Orlow <tony@lightlink.com>
wrote:

Lester Zick wrote:

On Sun, 27 May 2007 19:50:44 -0400, Tony Orlow <tony@lightlink.com>
wrote:

You have to start with some assumptions. What makes you think there is
such a thing as truth? You assume so.

If you only start with one assumption, it's pretty damn near impossible
to prove ANYTHING beyond that one assumption.

Tony, you know just a few days ago I posted a thread on exactly this
topic called "The Fable of the Empiric and the Truth Fairy" which
covers this objection. If you assume more than one assumption you
demonstrate the truth of one assumption in terms of the other. Then
you haven't demonstrated the truth of either. However if you assume
one assumption and demonstrate the truth of that one assumption in
terms of itself you get to make another single assumption to prove.

I don't refuse to consider it. I just don't see any demonstration for
those two truth values universally. It's a problem in complexity. On
the simplest level there are two alternatives "not" and "not not" one
true and the other false. You just don't show there are only the two
alternatives on more complex levels.

If you can do better than that go right ahead. Just don't expect to
hand me a bunch of things labeled true and false and expect me to
agree with your assumptions.

~v~~

You're the one who just said, "the two are mechanically exhaustive
of the possibilities for truth". What do you intend to do with those
possibilities?

I intend to compound them in various ways among other things to
produce the conjunctions "and" and "or". The fact that they are
mechanically exhaustive in terms of one another doesn't mean they
remain mechanically exhaustive through various compoundings.
~v~~
.

User: "Tony Orlow"
Title: Re: Infinitesimal Arithmetic	30 May 2007 10:30:46 PM

Lester Zick wrote:

On Tue, 29 May 2007 13:16:06 -0400, Tony Orlow <tony@lightlink.com>
wrote:

Lester Zick wrote:

On Sun, 27 May 2007 19:50:44 -0400, Tony Orlow <tony@lightlink.com>
wrote:

You have to start with some assumptions. What makes you think there is
such a thing as truth? You assume so.

If you only start with one assumption, it's pretty damn near impossible
to prove ANYTHING beyond that one assumption.

Tony, you know just a few days ago I posted a thread on exactly this
topic called "The Fable of the Empiric and the Truth Fairy" which
covers this objection.

You might want to stick with one conversation, and actually finish it
once in a while.
If you assume more than one assumption you

demonstrate the truth of one assumption in terms of the other.

Not if they are independent. Then, they can be compounded into, say,
theorems. You can actually prove things using the combination of facts,
and rules for combining them called logic
Then

you haven't demonstrated the truth of either. However if you assume
one assumption and demonstrate the truth of that one assumption in
terms of itself you get to make another single assumption to prove.

If you derive one conclusion from only one assumption, then the
conclusion and the assumption are equivalent statements. Does anyone
disagree with that?

I don't refuse to consider it.

Yeah, you have.
I just don't see any demonstration for

those two truth values universally.

Is there a third alternative, in the "universe"?
It's a problem in complexity.
Yeah, like, powers of two. The power set, it's commonly called.
On

the simplest level there are two alternatives "not" and "not not" one
true and the other false. You just don't show there are only the two
alternatives on more complex levels.

On the simplest level there is true and false, and "not" is defined as
true=not(false) and false=not(true). Grok it, Lester. That's THE
one-place logical operator.

If you can do better than that go right ahead. Just don't expect to
hand me a bunch of things labeled true and false and expect me to
agree with your assumptions.

~v~~

You're the one who just said, "the two are mechanically exhaustive
of the possibilities for truth". What do you intend to do with those
possibilities?

I intend to compound them in various ways among other things to
produce the conjunctions "and" and "or".

Then start with them, and then introduce "not" as an operator on them.
The fact that they are

mechanically exhaustive in terms of one another doesn't mean they
remain mechanically exhaustive through various compoundings.

~v~~

They exhaust the possibilities of truth in the Boolean sense, but of
course in the "real" world, numbers lie between 0 and 1.
01oo
.

User: "Lester Zick"
Title: Re: Infinitesimal Arithmetic	31 May 2007 06:48:31 PM

On Wed, 30 May 2007 23:30:46 -0400, Tony Orlow <tony@lightlink.com>
wrote:

Lester Zick wrote:

On Tue, 29 May 2007 13:16:06 -0400, Tony Orlow <tony@lightlink.com>
wrote:

Lester Zick wrote:

On Sun, 27 May 2007 19:50:44 -0400, Tony Orlow <tony@lightlink.com>
wrote:

You have to start with some assumptions. What makes you think there is
such a thing as truth? You assume so.

If you only start with one assumption, it's pretty damn near impossible
to prove ANYTHING beyond that one assumption.

Tony, you know just a few days ago I posted a thread on exactly this
topic called "The Fable of the Empiric and the Truth Fairy" which
covers this objection.

You might want to stick with one conversation, and actually finish it
once in a while.

Yeah and it would take forever.

If you assume more than one assumption you
demonstrate the truth of one assumption in terms of the other.

Not if they are independent.

I agree not if they are truly independent.

Then, they can be compounded into, say,
theorems. You can actually prove things using the combination of facts,
and rules for combining them called logic

Sure but you can't demonstrate the actual truth of theorems using
independent assumptions which you can't demonstrate true.

Then
you haven't demonstrated the truth of either. However if you assume
one assumption and demonstrate the truth of that one assumption in
terms of itself you get to make another single assumption to prove.

If you derive one conclusion from only one assumption, then the
conclusion and the assumption are equivalent statements. Does anyone
disagree with that?

Can you demonstrate the truth of what you say without demonstrating
the truth of the assumptions you use?

I don't refuse to consider it.

Yeah, you have.

Good. Then there's nothing to discuss.

I just don't see any demonstration for

those two truth values universally.

Is there a third alternative, in the "universe"?

It's a problem in complexity.

Yeah, like, powers of two. The power set, it's commonly called.

On

the simplest level there are two alternatives "not" and "not not" one
true and the other false. You just don't show there are only the two
alternatives on more complex levels.

On the simplest level there is true and false, and "not" is defined as
true=not(false) and false=not(true). Grok it, Lester. That's THE
one-place logical operator.

If you can do better than that go right ahead. Just don't expect to
hand me a bunch of things labeled true and false and expect me to
agree with your assumptions.

~v~~

You're the one who just said, "the two are mechanically exhaustive
of the possibilities for truth". What do you intend to do with those
possibilities?

I intend to compound them in various ways among other things to
produce the conjunctions "and" and "or".

Then start with them, and then introduce "not" as an operator on them.

I already have. You just weren't paying attention.

The fact that they are

mechanically exhaustive in terms of one another doesn't mean they
remain mechanically exhaustive through various compoundings.

~v~~

They exhaust the possibilities of truth in the Boolean sense, but of
course in the "real" world, numbers lie between 0 and 1.

Whatever, Tony. Since you're taking the credit for the traffic on my
threads why don't you just tell us all about everything whose truth
you assume but can't demonstrate?
~v~~
.

User: "Lester Zick"
Title: Re: Infinitesimal Arithmetic	27 May 2007 01:44:07 PM

On Sun, 27 May 2007 11:25:21 -0400, Tony Orlow <tony@lightlink.com>
wrote:

Well actually they consider me a crackpot by virtue of the fact that I
don't agree with them not that what I say isn't true. Big deal. How
could one expect otherwise when a uniform paradigmatic basis for truth
and agreement is absent? All their wailing and gnashing of teeth
really amounts to is a lamentation to the effect I don't agree with
them and am presumptuous enough to hold truth as the only criterion of
science not contrary conventions and their approval.

I've tried to discuss the basic mechanics of truth with you, but you
don't seem interested. I guess that makes ME stupid and lazy, eh?

Not necessarily. It just makes my effort to discuss it with you wasted
unless someone else out there has gotten some benefit.
~v~~
.

User: "Lester Zick"
Title: Re: Infinitesimal Arithmetic	27 May 2007 01:54:05 PM

On Sun, 27 May 2007 11:25:21 -0400, Tony Orlow <tony@lightlink.com>
wrote:

Well you have to understand that this has been going on for the last
two and a half years and you've only just gotten here. So I've been
pretty thoroughly routinized to all the reactionary personalities and
knee jerk responses of which yours was not uncharacteristic. You just
assumed what you knew was sufficiently true as to be unassailable.
It's what distinguishes you as an empiric from me as a scientist that
your arguments rely on assumptions of truth whereas my arguments rely
on demonstrations of truth instead. My demonstrations may be incorrect
but at least they are critically reviewable demonstrations.

Except that you don't explain yourself well enough to be critically
reviewed, and requests for clarification, as simple as a yes or no, go
unanswered.

What makes you think anyone could or should answer yes or no to your
assumptions of truth, Tony? That would make someone else the aribiter
of your own techniques of assumption and that's your job not mine. The
best one can do is to demonstrate the truth of ones assumptions and
ask whether a demonstration is true or not or in accordance with other
demonstrations of truth in other contexts. Which is what I do. I don't
demand others satisfy my assumptions of truth with respect to their
assumptions of truth.

So, that kinda disingenuous, dear Lester. Sorry to be so blunt.

Candor is all you have left at this juncture, Tony, not truth.
~v~~
.

User: "Lester Zick"
Title: Re: Infinitesimal Arithmetic	27 May 2007 01:42:00 PM

On Sun, 27 May 2007 11:25:21 -0400, Tony Orlow <tony@lightlink.com>
wrote:

and that people with years of training in these
areas might possibly know what they are talking about?

I don't doubt they do know exactly what they are talking about. They
just don't have any substantial idea what I'm talking about or whether
what they're talking about is actually true or just an educated guess.
Your own ignorance of the very idea of actual, literal truth is more
than indicative of that. How can a problematic paradigm possibly be
maintained without knowing it's true? So people with years of training
don't bother me at all when they're ignorant of what's true and how to
demonstrate that truth.

You talk about science in your usual vague terms. Why don't you try
defining exactly what you think the scientific method is? That might be
a good exercise.

Because my efforts with you have obviously been a complete waste
unless someone else out there auditing the material has gotten some
benefit.
~v~~
.

User: "Tony Orlow"
Title: Re: Infinitesimal Arithmetic	27 May 2007 06:52:40 PM

Lester Zick wrote:

On Sun, 27 May 2007 11:25:21 -0400, Tony Orlow <tony@lightlink.com>
wrote:

and that people with years of training in these
areas might possibly know what they are talking about?

You talk about science in your usual vague terms. Why don't you try
defining exactly what you think the scientific method is? That might be
a good exercise.

Because my efforts with you have obviously been a complete waste
unless someone else out there auditing the material has gotten some
benefit.

~v~~

Then tell the World. They are reading avidly. Explain the meaning of
science, if not for my education, then for theirs.
01oo
.

User: "Lester Zick"
Title: Re: Infinitesimal Arithmetic	28 May 2007 05:04:15 PM

On Sun, 27 May 2007 19:52:40 -0400, Tony Orlow <tony@lightlink.com>
wrote:

Lester Zick wrote:

On Sun, 27 May 2007 11:25:21 -0400, Tony Orlow <tony@lightlink.com>
wrote:

and that people with years of training in these
areas might possibly know what they are talking about?

You talk about science in your usual vague terms. Why don't you try
defining exactly what you think the scientific method is? That might be
a good exercise.

Because my efforts with you have obviously been a complete waste
unless someone else out there auditing the material has gotten some
benefit.

~v~~

Then tell the World. They are reading avidly. Explain the meaning of
science, if not for my education, then for theirs.

If it hasn't been explained in some ten thousand posts good luck.
~v~~
.

User: "G. Frege nomail@invalid"
Title: Re: Infinitesimal Arithmetic	24 May 2007 07:09:59 PM

On Thu, 24 May 2007 16:57:47 -0700, Lester Zick
<dontbother@nowhere.net> wrote:

Please tell us more about your "infinitesimal arithmetic".
What are the basic axioms and definitions of this theory?

r+i=r

I see. Ok. EOD.
.

User: "Lester Zick"
Title: Re: Infinitesimal Arithmetic	25 May 2007 04:55:48 PM

On Fri, 25 May 2007 02:09:59 +0200, G. Frege <nomail@invalid> wrote:

On Thu, 24 May 2007 16:57:47 -0700, Lester Zick
<dontbother@nowhere.net> wrote:

Please tell us more about your "infinitesimal arithmetic".
What are the basic axioms and definitions of this theory?

r+i=r

I see. Ok. EOD.

EO what D? So far you've only been testifying.
~v~~
.

User: "Jonathan Hoyle"
Title: Re: Infinitesimal Arithmetic	22 May 2007 10:19:10 PM

On May 22, 2:28 pm, Lester Zick <dontbot...@nowhere.net> wrote:

On 22 May 2007 08:01:02 -0700, Jonathan Hoyle <jonho...@mac.com>
wrote:

Well not exactly. If I+i=I does that mean i=0? Not hardly.

That's precisely what it means.

No. Any finite added to a transfinite produces the same transfinite
result.

That's not true either, not always anyway. If + is standard or
ordinal addition, I+i=I implies i=0, even if I is infinite. Only if +
is cardinal addition and I is infinite can you have I+i=I with non-
zero i.

No mystery here that I can see. The last case is what I had in mind.

That's why the arithmetic is transfinite to begin with. Unless
you're contending that the term "arithmetic" only applies to finites.
Which is a position I can understand and sympathize with.

That is not my contention. I was addressing infinitessimal
arithmetic, and since cardinal addition is not defined upon

Yeah, look, I don't really understand this usage "define upon". Either
something is defined or not. There is no "upon".

Of course there is an upon. For addition, + is defined upon numbers,
so that "2 + 2" but "2 + dog" does not.

I'm still trying to understand what your point is. If you can add
finites and infinites I see no reason you can't add infinitesimals and
finites. I mean as far as I can tell it's not a crime against nature
like division by zero.

Of course you can. But there are different types of addition.
Ordinal addition is different from cardinal addition which is
different still from hyper-real addition. Depending on which of these
operations you are talking about, an infinite number may or may not
grow when a finite number is added to it.

But when the term "arithmetic" is applied to any combination of
transfinites, infinitesimals, and finites you're not doing finite arithmetic
anymore and the rules are different.

You do not appear to be aware of the "rules" yourself.

I'm not exactly sure who is aware of what rules since I just brought
the subject up and you're telling me the subject is undefined in
mathematical terms. I'm still trying to make up my mind on the
mechanical rationale involved in infinitesimal/finite addition.

Addition is not something you "make your mind up" about. It is
something mathematical proven. The subject is not undefined; you are
simply not defining what you mean. Your remarks are the mathematical
equivalent too a bad pun.

The answer is
uniquely determined by simply stating what type of addition your "+"
is referring to.

I did. You don't know what I'm talking about but you don't like it
irregardless. Big deal.

My liking it or not is irrelevant. What matters is what is
mathematically correct. You have not defined what you are talking
about.

In hyper-real arithmetic (which is the arithmetic
defined on infinitessimals), I+i=I implies i=0, regaardless of the
size of I.

Gee that's just swell. Thanks for the input. When I get around to
hyper real arithmetic I'll be in touch. Noncewise I'd just prefer to
get back to the subject at hand if you don't mind or even if you do.

I presumed that you were discussing hyper-real addition, since that is
the only addition operation that is defined for infinitessimals.

Oh well now I'm beginning to take your point. You're just an *****
trying to explain that you're an ***** without saying so. A Kodak
moment no doubt.

I am sorry you are frustrated, but your sloppy use of terminology
makes it very confusing to know what you are saying. The only area of
mathematics where infinitessimals are defined is in Non-Standard
Analysis, inside the hyper-real line. If that is not what you have in
mind, then you need to define these infinitessimals are that you are
talking about, and what your + symbol means.
Regards,
Jonathan Hoyle
Eastman Kodak
.

User: "Lester Zick"
Title: Re: Infinitesimal Arithmetic	23 May 2007 06:01:03 PM

On 22 May 2007 20:19:10 -0700, Jonathan Hoyle <jonhoyle@mac.com>
wrote:

You do not appear to be aware of the "rules" yourself.

Addition is not something you "make your mind up" about.

Good. Then we can put the subject to rest.

It is
something mathematical proven. The subject is not undefined; you are
simply not defining what you mean. Your remarks are the mathematical
equivalent too a bad pun.

You speak as if you held the exclusive right to mathematical truth.
You can't demonstrate what you say is actually true and you can't
demonstrate the truth of mathematical axioms you assume true.
~v~~
.

User: "Jonathan Hoyle"
Title: Re: Infinitesimal Arithmetic	23 May 2007 09:04:43 PM

You speak as if you held the exclusive right to mathematical truth.

No exclusivity here. I am merely sharing what has already been proven
for some time now.

You can't demonstrate what you say is actually true and you can't
demonstrate the truth of mathematical axioms you assume true.

What would you accept as a demonstration of the truth (or falsity) of
mathematical axioms?
Jonathan Hoyle
Eastman Kodak
.

User: "Lester Zick"
Title: Re: Infinitesimal Arithmetic	26 May 2007 02:03:22 PM

On 23 May 2007 19:04:43 -0700, Jonathan Hoyle <jonhoyle@mac.com>
wrote:

You speak as if you held the exclusive right to mathematical truth.

No exclusivity here. I am merely sharing what has already been proven
for some time now.

You can't demonstrate what you say is actually true and you can't
demonstrate the truth of mathematical axioms you assume true.

What would you accept as a demonstration of the truth (or falsity) of
mathematical axioms?

It's not a question of what I would accept; it's what would
demonstrate them true. It's called science.
~v~~
.

User: "Jonathan Hoyle"
Title: Re: Infinitesimal Arithmetic	26 May 2007 02:52:28 PM

What would you accept as a demonstration of the truth (or falsity) of
mathematical axioms?

It's not a question of what I would accept; it's what would
demonstrate them true. It's called science.

Fine. What would demonstrate them as true?
Jonathan Hoyle
Eastman Kodak
.

User: "Lester Zick"
Title: Re: Infinitesimal Arithmetic	27 May 2007 02:18:50 PM

On 26 May 2007 12:52:28 -0700, Jonathan Hoyle <jonhoyle@mac.com>
wrote:

What would you accept as a demonstration of the truth (or falsity) of
mathematical axioms?

It's not a question of what I would accept; it's what would
demonstrate them true. It's called science.

Fine. What would demonstrate them as true?

Demonstrably true axioms would have to be based on differences,
differences between differences, etc. instead of addition and sums.
~v~~
.

User: "Tony Orlow"
Title: Re: Infinitesimal Arithmetic	27 May 2007 06:58:23 PM

Lester Zick wrote:

On 26 May 2007 12:52:28 -0700, Jonathan Hoyle <jonhoyle@mac.com>
wrote:

What would you accept as a demonstration of the truth (or falsity) of
mathematical axioms?

It's not a question of what I would accept; it's what would
demonstrate them true. It's called science.

Fine. What would demonstrate them as true?

Demonstrably true axioms would have to be based on differences,
differences between differences, etc. instead of addition and sums.

~v~~

So, you like derivatives, but not integrals? Do you like dandelions but
not irises, and dung beetles but not inch worms?
01oo
.

User: "Lester Zick"
Title: Re: Infinitesimal Arithmetic	28 May 2007 01:28:06 PM

On Sun, 27 May 2007 19:58:23 -0400, Tony Orlow <tony@lightlink.com>
wrote:

Lester Zick wrote:

On 26 May 2007 12:52:28 -0700, Jonathan Hoyle <jonhoyle@mac.com>
wrote:

What would you accept as a demonstration of the truth (or falsity) of
mathematical axioms?

It's not a question of what I would accept; it's what would
demonstrate them true. It's called science.

Fine. What would demonstrate them as true?

Demonstrably true axioms would have to be based on differences,
differences between differences, etc. instead of addition and sums.

~v~~

So, you like derivatives, but not integrals? Do you like dandelions but
not irises, and dung beetles but not inch worms?

But even more I like posts with substance.
~v~~
.

User: "Jonathan Hoyle"
Title: Re: Infinitesimal Arithmetic	27 May 2007 11:32:44 PM

On May 27, 3:18 pm, Lester Zick <dontbot...@nowhere.net> wrote:

Demonstrably true axioms would have to be based on differences,
differences between differences, etc. instead of addition and sums.

And why is that, Lester? Is it because you say so?
Jonathan Hoyle
Eastman Kodak
.

User: "Lester Zick"
Title: Re: Infinitesimal Arithmetic	28 May 2007 02:02:25 PM

On 27 May 2007 21:32:44 -0700, Jonathan Hoyle <jonhoyle@mac.com>
wrote:

On May 27, 3:18 pm, Lester Zick <dontbot...@nowhere.net> wrote:

Demonstrably true axioms would have to be based on differences,
differences between differences, etc. instead of addition and sums.

And why is that, Lester? Is it because you say so?

Well technically, Jonathan, you asked what not why so I decided to
restrict my reply to the bare minimum. You have to understand that
I've been arguing and demonstrating for the last two and a half years.
The point can be most easily made by simply noting that "not not" is
universally self contradictory and tautological alternatives must be
true. In other words "not" is true of everything because "not not" is
self contradictory, which I take to mean false, and the combination of
"not not" and "not" is mechanically exhaustive of all possibilities
for truth and falsity.
However there are also collateral interpretations of "not" in various
forms such as "contradiction" and the "contradiction of contradiction"
"differences" and "different from differences (which I consider most
applicable to math) "alternatives" and "alternative to alternatives"
which are all comparably exhaustive as well.
This is why I suggested reading the brief root post to my thread
"Epistemology 401: Tautological Mechanics" where I demonstrate the
origin of "and" and "or" conjunctions purely in terms of compoundings
of "not". And if you have the stomach for it you might also consider
perusing the root post to my thread "Epistemology 201: The Science of
Science". The latter is several pages but the thread in its entirety
runs maybe ten thousand posts and is arguably the most trafficked
thread in the history of the usenet.
I'm happy to answer specific questions but I can't really reargue the
whole subject to everyones satisfaction.
~v~~
.

User: "Jonathan Hoyle"
Title: Re: Infinitesimal Arithmetic	28 May 2007 04:01:29 PM

On May 28, 3:02 pm, Lester Zick <dontbot...@nowhere.net> wrote:

I presume that during this two and a half year period, your success
rate has been about the same as it has been in this thread?

The point can be most easily made by simply noting that "not not" is
universally self contradictory and tautological alternatives must be
true.

??? Are you referring to the logical principle of double negation as
tautology? Are you arguing against the truth of this? If so, you
might find some comfort by speaking with constructivists who deny the
Law of the Excluded Middle.

In other words "not" is true of everything because "not not" is
self contradictory, which I take to mean false, and the combination of
"not not" and "not" is mechanically exhaustive of all possibilities
for truth and falsity.

This is poor worded, and even more poorly thought out. One would have
guessed that in two and a half years you would have had the
opportunity to think about this more caarefully.

However there are also collateral interpretations of "not" in various
forms such as "contradiction" and the "contradiction of contradiction"
"differences" and "different from differences (which I consider most
applicable to math) "alternatives" and "alternative to alternatives"
which are all comparably exhaustive as well.

Have you considered taking any courses in symbolic logic? That might
help clear up some of your concerns.

This is why I suggested reading the brief root post to my thread
"Epistemology 401: Tautological Mechanics" where I demonstrate the
origin of "and" and "or" conjunctions purely in terms of compoundings
of "not". And if you have the stomach for it you might also consider
perusing the root post to my thread "Epistemology 201: The Science of
Science". The latter is several pages but the thread in its entirety
runs maybe ten thousand posts and is arguably the most trafficked
thread in the history of the usenet.

I have not had the opportunity to wade through those posts, although I
can only imagine the responses you've gotten. If I have the time, I
will look them up and respond then. Regardless, I reiterate my
recommendation to take a logic course. It would dramaticaally improve
your ability to be able to converse.

I'm happy to answer specific questions but I can't really reargue the
whole subject to everyones satisfaction.

You are not likely to satify everyone prior to improving your logic
skills.
Good Luck,
Jonathan Hoyle
Eastman Kodak
.

User: "Lester Zick"
Title: Re: Infinitesimal Arithmetic	28 May 2007 07:36:08 PM

On 28 May 2007 14:01:29 -0700, Jonathan Hoyle <jonhoyle@mac.com>
wrote:

Have you considered taking any courses in symbolic logic? That might
help clear up some of your concerns.

Jesus! What do you think I'm still in the sixth grade or something?
Don't partonize me. Go back to counting the number of pixels in truth.
~v~~
.

User: "Jonathan Hoyle"
Title: Re: Infinitesimal Arithmetic	28 May 2007 11:01:08 PM

Have you considered taking any courses in symbolic logic? That might
help clear up some of your concerns.

Jesus! What do you think I'm still in the sixth grade or something?
Don't partonize me. Go back to counting the number of pixels in truth.

What I am talking about is not a sixth grade course. Symbolic Logic
is taught at the undergraduate level at most colleges, and I recommend
it to you because you seem to be very passionate about these things.
I am not trying to be patronizing. I sincerely think that if you take
such a course, you will understand these thing better.
Happy Memorial Day,
Jonathan Hoyle
Eastman Kodak
.

User: "Lester Zick"
Title: Re: Infinitesimal Arithmetic	29 May 2007 01:39:21 PM

On 28 May 2007 21:01:08 -0700, Jonathan Hoyle <jonhoyle@mac.com>
wrote:

Have you considered taking any courses in symbolic logic? That might
help clear up some of your concerns.

Jesus! What do you think I'm still in the sixth grade or something?
Don't partonize me. Go back to counting the number of pixels in truth.

And the very sincerity and earnestness are what make you patronizing
and condescending. What makes you think I haven't taken the courses?
That I don't talk and reason like you? When I ask you how many pixels
there are in truth or criticize your inept spelling and composition
skills it's merely hyperbolic rhetorical irony designed as such and if
you don't want to do anything about them that's your business. But
when you assume I haven't already taken courses at the undergraduate
level and simply disagree with the approach, it represents the height
of condescension.And that kind of naive assumption of truth is exactly
what delineates you as a mathematiker and empiric to begin with.
What makes you think you can ride in here on your hobby horse and
simply declare dr and dt aren't infinitesimals then turn right around
and use the very same concept of infinitesimals to define the standard
approach to the definition of derivatives. I certainly appreciate your
courtesy in presenting the definition clearly and succinctly but don't
tell me I can't do one thing then turn around and use it yourself.
Your explanation of the standard approach:

STANDARD APPROACH:
The derivative is defined in terms of limits, not infinitesimals:

f'(x) = lim t->x [f(t) - f(x)] / (t-x) = lim t->x [t^2 - x^2] / (t-x)
= lim t->x (t+x)(t-x)/(t-x)
= lim t->x (t+x) = (x+x) = 2x.

Note that no infinitesimals were assumed to exist in this proof. The
calculation is just as easy, and it is more obvious what the intention

Now as t->x what makes you think "(t-x)" is not an infinitesimal just
because the whole expression represents a limit?
And as t->x what makes you think "[f(t)-f(x)]" is not an infinitesimal
as well for that matter?
And what are you actually doing in defining the limit except simple
division?
And if you're entitled to use infinitesimals in defining derivatives I
see no conceivable reason I shouldn't be able to do definite integrals
the converse way using infinitesimals dr and dt with multiplication.
I say dr and dt; you say "[f(t)-f(x)]" and "(t-x)". So what? As t->x
they look like the same basic concept to me. And if it walks like a
duck and quacks like a duck . . .
Your problem with Newtonian infinitesimals may be reasonable. I'm not
enough of a mathematics historian to assess such nuanic distinctions
without considerably more study. But I pose certain specific questions
to you regarding the mechanics of t->x and the length of time needed
for any rotation of r and you simply ignore them then complain I need
to re educate myself at the undergraduate level regarding subjects you
can't demonstrate I haven't discarded for cause. Very partronizing.
~v~~
.

User: "Randy Poe"
Title: Re: Infinitesimal Arithmetic	29 May 2007 12:17:59 AM

On May 28, 5:36 pm, Lester Zick <dontbot...@nowhere.net> wrote:

On 28 May 2007 14:01:29 -0700, Jonathan Hoyle <jonho...@mac.com>
wrote:

Have you considered taking any courses in symbolic logic? That might
help clear up some of your concerns.

Jesus! What do you think I'm still in the sixth grade or something?

Something like that.

Don't partonize me. Go back to counting the number of pixels in truth.

You think nobody takes courses beyond sixth grade? Perhaps
that's your problem. There's really no stigma with taking courses
as an adult, you know.
- Randy
.

User: "Lester Zick"
Title: Re: Infinitesimal Arithmetic	29 May 2007 01:43:18 PM

On 28 May 2007 22:17:59 -0700, Randy Poe <poespam-trap@yahoo.com>
wrote:

On May 28, 5:36 pm, Lester Zick <dontbot...@nowhere.net> wrote:

On 28 May 2007 14:01:29 -0700, Jonathan Hoyle <jonho...@mac.com>
wrote:

Have you considered taking any courses in symbolic logic? That might
help clear up some of your concerns.

Jesus! What do you think I'm still in the sixth grade or something?

Something like that.

Yeah, yeah, yeah, Randy. Really witty. It's just that I'm witty and
you're not. Now we see why. Too bad you don't have quite as much to
say about demonstrations of truth for your assumptions of truth.

Don't partonize me. Go back to counting the number of pixels in truth.

You think nobody takes courses beyond sixth grade? Perhaps
that's your problem. There's really no stigma with taking courses
as an adult, you know.

Sure like ESL and remedial english for most mathematikers.
~v~~
.

User: "Randy Poe"
Title: Re: Infinitesimal Arithmetic	29 May 2007 08:57:18 PM

On May 29, 11:43 am, Lester Zick <dontbot...@nowhere.net> wrote:

On 28 May 2007 22:17:59 -0700, Randy Poe <poespam-t...@yahoo.com>
wrote:

On May 28, 5:36 pm, Lester Zick <dontbot...@nowhere.net> wrote:

On 28 May 2007 14:01:29 -0700, Jonathan Hoyle <jonho...@mac.com>
wrote:

Have you considered taking any courses in symbolic logic? That might
help clear up some of your concerns.

Jesus! What do you think I'm still in the sixth grade or something?

Something like that.

Yeah, yeah, yeah, Randy. Really witty. It's just that I'm witty and
you're not.

Did you know that declaring "I'm witty" will not actually cause
people to perceive you as witty?

You think nobody takes courses beyond sixth grade? Perhaps
that's your problem. There's really no stigma with taking courses
as an adult, you know.

Sure like ESL and remedial english for most mathematikers.

Like college courses. You really think all the knowledge you needed
in life ended at 6th grade?
- Randy
.

User: "Lester Zick"
Title: Re: Infinitesimal Arithmetic	30 May 2007 01:34:47 PM

On 29 May 2007 18:57:18 -0700, Randy Poe <poespam-trap@yahoo.com>
wrote:

On May 29, 11:43 am, Lester Zick <dontbot...@nowhere.net> wrote:

On 28 May 2007 22:17:59 -0700, Randy Poe <poespam-t...@yahoo.com>
wrote:

On May 28, 5:36 pm, Lester Zick <dontbot...@nowhere.net> wrote:

On 28 May 2007 14:01:29 -0700, Jonathan Hoyle <jonho...@mac.com>
wrote:

Have you considered taking any courses in symbolic logic? That might
help clear up some of your concerns.

Jesus! What do you think I'm still in the sixth grade or something?

Something like that.

Yeah, yeah, yeah, Randy. Really witty. It's just that I'm witty and
you're not.

Did you know that declaring "I'm witty" will not actually cause
people to perceive you as witty?

Never thought it mattered to anyone but you.

You think nobody takes courses beyond sixth grade? Perhaps
that's your problem. There's really no stigma with taking courses
as an adult, you know.

Sure like ESL and remedial english for most mathematikers.

Like college courses. You really think all the knowledge you needed
in life ended at 6th grade?

No. I think all the knowledge you needed did.
~v~~
.

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