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Kris Warkentin

Re: Tirade (offtopic) "It's been done"

You saw the original "proof" didn't you? The one with the 10 and the 9 was
just to show that it's kind of silly. It isn't a proof but rather an
illustration. I think that a lot of background work is required to show
that 0.9999.... is exactly equal to one and given that background, Angela's
proof is sufficient. Your demonstration is just as silly as mine since
alpha being an infinitesemly [sp?] small value means that it is exactly
equivalent to zero right?

RK had cleverly pointed out that using different numerical bases can
demonstrate these things too. In base 3, 0.1 = 1/3 and 0.1 + 0.1 + 0.1 = 1.
Anyway, I'm afraid that the 'proof' I clipped from Slashdot was not
mathematically rigorous enough for this audience. (Wow! Tough crowd...take
my wife, please.... but I think it did serve it's original purpose of
satisfying RK.

Kris

"ed1k" <ed1k@spamerstrap.com> wrote in message
news:01c211eb\$d97c8b80\$106fa8c0@ED1K...
ed1k <ed1k@spamerstrap.com> wrote in article
01c211eb\$15493060\$106fa8c0@ED1K>...
x = (9 - 9*x) / 9 = [9*(1 - alpha)] / 9 = 1- alpha,
^^^^^^^^
sorry, it should be

x = (9 - 9 * alpha)/9

--
Eduard.
ed1k at ukr dot net

Bill Caroselli (Q-TPS)

Re: Tirade (offtopic) "It's been done"

OMG! That takes me back. Wasn't there an argument about quality being
subjective as opposed to objective or something like that. I can remember
talking about that crap for months back when I was in school.

"Kris Warkentin" <kewarken@qnx.com> wrote in message
news:ae2gof\$9ar\$1@nntp.qnx.com...
That's interesting and sort of ties in with a book I've just started
reading. "Zen and the Art of Motorcycle Maintenance", by Robert M.
Pirsig.
One of his hypothesis is that 'quality', as such, cannot be defined other
than by saying, "You know it when you see it". One can prove it's
existance
simply by observing the world around us and how we react to various
things.
One can observe it's importance simply by contemplating what the world
would
be like if there were no such concept. ie. Would we have all these
varieties of food if 'quality' didn't exist or would we just eat that
which
provided sufficient nutrition? Would people be interested in observing
sporting events? Trying to pin it down is much more difficult though.
Dijkstra's definition of mathematical elegance is simply, "That which is
recognized as beautiful by a mathematician".

Kris

Wojtek Lerch

Re: Tirade (offtopic) "It's been done"

Kris Warkentin <kewarken@qnx.com> wrote:
Didn't someone say that parallel lines are lines that cross infinitely far away?
I've heard a few people say it. But I don't think I've ever hear a
mathematician say it...

--
Wojtek Lerch QNX Software Systems Ltd.

Chris Wiebe

Re: Tirade (offtopic) "It's been done"

Actually, Quality (with a capital Q) is neither objective nor subjective,
but comes before...

The first time I read ZAMM it was a truly mind-blowing experience (ok I was
young and impressionable). Read it again a few years ago. It's still
fascinating to read. There is also a sequel "Lila" that came out a few
years ago - but it IMHO it just didn't live up to the spirit of the
original. I'd highly recommend reading ZAMM if you're looking for a way to
break out of your cartesian mindset...

Dammit Kris now I'll have to read it again...

"Bill Caroselli (Q-TPS)" <QTPS@EarthLink.net> wrote in message
news:ae7s8d\$ccj\$1@inn.qnx.com...
OMG! That takes me back. Wasn't there an argument about quality being
subjective as opposed to objective or something like that. I can remember
talking about that crap for months back when I was in school.

"Kris Warkentin" <kewarken@qnx.com> wrote in message
news:ae2gof\$9ar\$1@nntp.qnx.com...
That's interesting and sort of ties in with a book I've just started
reading. "Zen and the Art of Motorcycle Maintenance", by Robert M.
Pirsig.
One of his hypothesis is that 'quality', as such, cannot be defined
other
than by saying, "You know it when you see it". One can prove it's
existance
simply by observing the world around us and how we react to various
things.
One can observe it's importance simply by contemplating what the world
would
be like if there were no such concept. ie. Would we have all these
varieties of food if 'quality' didn't exist or would we just eat that
which
provided sufficient nutrition? Would people be interested in observing
sporting events? Trying to pin it down is much more difficult though.
Dijkstra's definition of mathematical elegance is simply, "That which is
recognized as beautiful by a mathematician".

Kris

ed1k

Re: Tirade (offtopic) "It's been done"

Kris Warkentin <kewarken@qnx.com> wrote in article <ae7qgi\$d07\$1@nntp.qnx.com>...
Didn't someone say that parallel lines are lines
that cross infinitely far away?
Yeah, I said it here. I heard it at school (university) in some engineering course. It's good
"definition" for such debates
--
Eduard.
ed1k at ukr dot net

ed1k

Re: Tirade (offtopic) "It's been done"

Kris Warkentin <kewarken@qnx.com> wrote in article <ae7rir\$e3t\$1@nntp.qnx.com>...
You saw the original "proof" didn't you? The one with the 10 and the 9 was
just to show that it's kind of silly. It isn't a proof but rather an
illustration. I think that a lot of background work is required to show
that 0.9999.... is exactly equal to one and given that background, Angela's
proof is sufficient.
Sorry, I thought it said Willow, but not you Kris
Your demonstration is just as silly as mine since
alpha being an infinitesemly [sp?] small value means that it is exactly
equivalent to zero right?
No. Alpha isn't zero. Alpha is infinitesimal, alpha wants to be zero, but can't. Another course I
heard at university it was infinitesimal calculus. This sort of science is based on statement that
infinitesimal value is not zero

Infinitesimal is exactly equivalent to zero for engineers only But be careful to tread on
dangerous territory of Theory of inaccuracy (sorry for my english, might be this science has
another name in english spoken countries).
RK had cleverly pointed out that using different numerical bases can
demonstrate these things too. In base 3, 0.1 = 1/3 and 0.1 + 0.1 + 0.1 = 1.
1/3 + 1/3 + 1/3 = 3/3 = 1 . What's wrong? Don't you get this result by calculator?

I heard the base 3 is optimal for calculators. Don't remember the proof, but professor who
explained that stuff said the binary base is only technical issue at this moment, it's deadlock and
computers in future will only in base 3. Might be, he was just crazy...
Anyway, I'm afraid that the 'proof' I clipped from Slashdot was not
mathematically rigorous enough for this audience. (Wow! Tough crowd...take
my wife, please.... but I think it did serve it's original purpose of
satisfying RK.
I thought Robert had more serious purpose of this thread. I heard that Slashdot's proof many times
when was student. But I'm sorry to see you're mixing zero and infinitesimal.

P.S. Yet another puzzle:
Inquire some one "How many is 2 + 2 * 2?" People usually answer 8, but really it's 6. Try type 2 +
2 * 2 in windows calculator in scientific form and in standart form. Feel difference.
--
Eduard.
ed1k at ukr dot net

Andrzej Kocon

Re: Tirade (offtopic) "It's been done"

On Thu, 13 Jun 2002 09:36:06 -0700, Mitchell Schoenbrun
<maschoen@pobox.com> wrote:
This whole thread brings tears to my eyes. I recall vividly in
7th grade when my teacher was trying to get these ideas across.
(...)
It's not an unusual age for slashdot kids (the proof was taken
from there). No wonder they get excited "discovering" such ideas. It's
their turn...
(...)
So before going further it might help to know what a proof
is? At its most formal level, a proof would be a step by
step description of how one gets from one's primary
assumptions, postulates, to ones conclusion. Each step must
be justified by reference to either a postulate, or a
previously proved conclusion.
Plus explicit inference rules, ie., according to what logic
(not all systems are algebraic). Btw., some say that Euclid's axioms
don't suffice for the things we were taught at school as Euclidean
geometry...

To end in the spirit of this thread:

0.99999... - 0.9999... = 0
(0.99999 - 0.9999)... = 0
(0.00009)... = 0
... = 0

ako
Mitchell Schoenbrun --------- maschoen@pobox.com

Andrzej Kocon

Re: Tirade (offtopic) "It's been done"

On 13 Jun 2002 08:24:28 GMT, "ed1k" <ed1k@spamerstrap.com> wrote:
I heard the base 3 is optimal for calculators. Don't remember the proof, but professor who
explained that stuff said the binary base is only technical issue at this moment, it's deadlock and
computers in future will only in base 3. Might be, he was just crazy...
Wasn't it e (= 2.71...), a conclusion Atanasoff came to in
late 30's?

ako

Andrzej Kocon

Re: Tirade (offtopic) "It's been done"

On Wed, 12 Jun 2002 11:55:55 -0400, "Kris Warkentin"
<kewarken@qnx.com> wrote:
"Wojtek Lerch" <wojtek_l@yahoo.ca> wrote in message
news:ae5mnq\$o52\$1@nntp.qnx.com...
In calculus, there is a definition of what it means that a series or a
function does have a limit. I don't remember ever coming across such a
concept in geometry. I think your professor would have to define it
before he could come up with a proof.

And I doubt it would be easy to define it in a way that would make a
proof possible. Notice that no matter how big you make the circle,
only a finite section of the line is actually near the circle. The part
of the line that't near the circle grows as you grow the circle, but the
part that's far away from the circle doesn't shrink!

It's entirely possible that I'm just being silly but it's fun to speculate.
Another thing I was thinking about was taking an arc of a certain width from
a circle. Say I take a line of length 2. Then I make an arc on that line
that is part of a circle of some radius r. Now, if I start moving the
center of the circle away from me, the distance from the center of the line
to edge of the arc decreases. The angle of the arc also decreases so I have
a triangle (based on my original line) where the angle at the tip is
decreasing towards zero. Didn't someone say that parallel lines are lines
that cross infinitely far away? So using this method we can also construct
a triangle where two corners are 90 degrees each. Yeehaw!
1/8 of any sphere would do... (Since we didn't state the
premises, we're not confined to any kind of space).

ako
Kris

--
Wojtek Lerch QNX Software Systems Ltd.

Mitchell Schoenbrun

Re: Tirade (offtopic) "It's been done"

This whole thread brings tears to my eyes. I recall vividly in
7th grade when my teacher was trying to get these ideas across.
First he showed that 1/3 = .33333....

We had some trouble with this first venture into infinity,
but when he added .33333.... together three times and got
..99999.... there was a lot of discomfort in the room. How could
..99999.... = 1? It's always off a bit, isn't it.

Finally he went through the calculation described above as a
proof, and I was quite satisfied.

So before going further it might help to know what a proof
is? At its most formal level, a proof would be a step by
step description of how one gets from one's primary
assumptions, postulates, to ones conclusion. Each step must
be justified by reference to either a postulate, or a
previously proved conclusion.

Practically speaking however, proofs are almost always heavily
abbreviated. So for example when one writes

10x - 9x = x

It is not usually necessary to break it down as

1) 10x - 9x = (10 - 9)x (Distribution of addition over multiplication

2) (10 - 9)x = (1)x (Let's not get into it

3) (1)x = x (Identity property of 1

Each of the steps must be fully justified.
In our "proof" this would include the construction of the
integers from basic set theory. That's the step #2 didn't
want to get into.

Proving all the underlying assumptions in the "proof" that
has been provided would encompass a lot of college math.
This would require some basic analysis to get by the issue
of limits. That does not necessarily render our "proof"
incorrect. Also important I think is the context. In this
forum, this should be a perfectly reasonably proof. The
irony of bringing up the calculus of infintesimals is that
long before understanding this somewhat obscure subject, one
aught to be quite content with .99999.... == 1.

Mitchell Schoenbrun --------- maschoen@pobox.com

Kris Warkentin

Re: Tirade (offtopic) "It's been done"

Thanks Mitchell....I didn't think it was all that awful myself. I was
beginning to feel like a dartboard.

Kris

"Mitchell Schoenbrun" <maschoen@pobox.com> wrote in message
news:Voyager.020613093606.202A@schoenbrun.com...
This whole thread brings tears to my eyes. I recall vividly in
7th grade when my teacher was trying to get these ideas across.
First he showed that 1/3 = .33333....

We had some trouble with this first venture into infinity,
but when he added .33333.... together three times and got
.99999.... there was a lot of discomfort in the room. How could
.99999.... = 1? It's always off a bit, isn't it.

Finally he went through the calculation described above as a
proof, and I was quite satisfied.

So before going further it might help to know what a proof
is? At its most formal level, a proof would be a step by
step description of how one gets from one's primary
assumptions, postulates, to ones conclusion. Each step must
be justified by reference to either a postulate, or a
previously proved conclusion.

Practically speaking however, proofs are almost always heavily
abbreviated. So for example when one writes

10x - 9x = x

It is not usually necessary to break it down as

1) 10x - 9x = (10 - 9)x (Distribution of addition over multiplication

2) (10 - 9)x = (1)x (Let's not get into it

3) (1)x = x (Identity property of 1

Each of the steps must be fully justified.
In our "proof" this would include the construction of the
integers from basic set theory. That's the step #2 didn't
want to get into.

Proving all the underlying assumptions in the "proof" that
has been provided would encompass a lot of college math.
This would require some basic analysis to get by the issue
of limits. That does not necessarily render our "proof"
incorrect. Also important I think is the context. In this
forum, this should be a perfectly reasonably proof. The
irony of bringing up the calculus of infintesimals is that
long before understanding this somewhat obscure subject, one
aught to be quite content with .99999.... == 1.

Mitchell Schoenbrun --------- maschoen@pobox.com

Bill Caroselli (Q-TPS)

Re: Tirade (offtopic) "It's been done"

"Mitchell Schoenbrun" <maschoen@pobox.com> wrote in message
news:Voyager.020613093606.202A@schoenbrun.com...
This whole thread brings tears to my eyes. I recall vividly in
7th grade when my teacher was trying to get these ideas across.
First he showed that 1/3 = .33333....

We had some trouble with this first venture into infinity,
but when he added .33333.... together three times and got
.99999.... there was a lot of discomfort in the room. How could
.99999.... = 1? It's always off a bit, isn't it.

The problem we have with this is that IT is not "off a bit" but that the on
paper representation of it is off a bit.

When we write it we are choosing to take a short cut and deliberately not
showing as much detail as we know to be more correct. If we wrote .33333
don't we really know that .333333333 is more accurate. But when we add
those three dots and make it .333... then everyone knows that all of those
extra threes are really there. The number IS accurate. The paper
representation just has an admitted shortcut, as indicated by the three
dots. So in the end, it too is accurate.

ed1k

Re: Tirade (offtopic) "It's been done"

Andrzej Kocon <ako@box43.gnet.pl> wrote in article <3d086604.9882092@inn.qnx.com>...
Wasn't it e (= 2.71...), a conclusion Atanasoff came to in
late 30's?
No. It was some mechanical proof. He said about cogwheels, calculators and quantity of cogs in
different models I heard when computers were on vacuum tubes there was some computer with base
3 in USSR.
--
Eduard.
ed1k at ukr dot net

Bill Caroselli (Q-TPS)

Re: Tirade (offtopic) "It's been done"

"Andrzej Kocon" <ako@box43.gnet.pl> wrote in message
news:3d086585.9755602@inn.qnx.com...
To end in the spirit of this thread:

0.99999... - 0.9999... = 0
(0.99999 - 0.9999)... = 0
Isn't that exactly equal to 0.00009?

Kris Warkentin

Re: Tirade (offtopic) "It's been done"

"Bill Caroselli (Q-TPS)" <QTPS@EarthLink.net> wrote in message
news:aedb07\$ib9\$1@inn.qnx.com...
"Andrzej Kocon" <ako@box43.gnet.pl> wrote in message
news:3d086585.9755602@inn.qnx.com...

To end in the spirit of this thread:

0.99999... - 0.9999... = 0
(0.99999 - 0.9999)... = 0

Isn't that exactly equal to 0.00009?
Assuming any of that were legal, aren't the '...' at the end of the two
different? One is 9's going to infinity starting at 0.00009 and the other
starts at 0.000009 (one more zero). That would mean the factoring out the
'...' was illegal.

I can't believe I'm actually opening my mouth on this thread again. I must
be a masochist.

Kris