Tirade (offtopic) "It's been done"

QNX Newsgroups (Archives) qdn.cafe
81

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 :smiley:

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 :wink:

Infinitesimal is exactly equivalent to zero for engineers only :wink: 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…> :wink: > 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

82

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

83

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

84

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.

85

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

86

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

:wink:

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

87

“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.

88

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 :wink: I heard when computers were on vacuum tubes there was some computer with base
3 in USSR.

Eduard.
ed1k at ukr dot net

89

“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?

90

“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

91

Kris Warkentin <kewarken@qnx.com> wrote:

“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.

Just to add fuel to the fire; what happens when you take two laser beams,
and intersect them; say a meter from your current position. Then you gradually
move the intersection point further and further away, until the lines are almost
parallel.

Then, just for grins, you move the laser beams so that they are almost parallel
to each other. Then you move them further apart still. Do they suddenly cease
to intersect???

INQUIRING MINDS WANT TO KNOW!

Cheers,
-RK

(I have more :slight_smile: – Washing machines in vacuum with nothing else; relativity sez
that all motion is relative; at what point do the clothes stop “sticking” to the
inside edge?)

–
Robert Krten, PARSE Software Devices +1 613 599 8316.
Realtime Systems Architecture, Books, Video-based and Instructor-led
Training and Consulting at www.parse.com.
Email my initials at parse dot com.

92

Previously, Kris Warkentin wrote in qdn.cafe:

Assuming any of that were legal, aren’t the ‘…’ at the end of the two
different?

I think it was meant as a joke.


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

93

Previously, Robert Krten wrote in qdn.cafe:

Just to add fuel to the fire; what happens when you take two laser beams,
and intersect them; say a meter from your current position. Then you gradually
move the intersection point further and further away, until the lines are almost
parallel.

Then, just for grins, you move the laser beams so that they are almost parallel
to each other. Then you move them further apart still. Do they suddenly cease
to intersect???

INQUIRING MINDS WANT TO KNOW!

Well, you asked for it. Lets assume for a second that you
had two perfectly collaminated lasers. That is the beams
can go indefinitely. Now assume that the device that is
cranking them closer and closer to parallel is quantized in
its movements. This of course has to be the case, but lets not
get into it. And just for fun, assume that there is one last “crank”
that puts the beams into their final exactly parallel mode.
Ok, so you execute this crank and point where the beams intersect
now moves outward at the speed of light. so what you have is something
that looks like this:

/
/
------------------------------------------\ /
/
/
------------------------------------------/
\

So that point heads for the edge of the universe, which it does
not ever reach.


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

94

I just happened to be reading something that you might find interesting.

Apparently there were 5 postulates of Euclidian geometry, the fifth of which
was that for a given point, only one parallel line could pass through it.
That is, parallel lines never meet.

Except that Bolyai and Lobachevski showed that a proof of the fifth
postulate was impossible.

And a German named Riemann came up with another system of geometry that also
contradicted Euclid’s first axiom: that only one line can pass through any
two points.

According to this book (which may not be the final authority on the subject
I’ll admit), Riemann’s geometry is thought to most accurately describe our
world. Oddly enough, the book is ‘Zen and the Art of Motorcycle
Maintenance’ which creates a rather strange link to another part of this
thread. Funny. Coincidence? Or not…

:wink:

Kris

“Wojtek Lerch” <wojtek_l@yahoo.ca> wrote in message
news:ae86qc$m9r$1@nntp.qnx.com…

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.

95

On Sat, 15 Jun 2002 22:25:32 -0400, “Kris Warkentin”
<kewarken@qnx.com> wrote:

I just happened to be reading something that you might find interesting.

Certainly, although for the things quoted I’d prefer other
types of books. Since our discipline is highly mathematical, never too
much of it (preferably before any course on programming). There are
some unclear points, however:

Apparently there were 5 postulates of Euclidian geometry, the fifth of which
was that for a given point, only one parallel line could pass through it.

For a given line and a point outside it on a given plane.

That is, parallel lines never meet.

That is somewhat circular definition…

Except that Bolyai and Lobachevski showed that a proof of the fifth
postulate was impossible.

One does not prove postulates, at most their consistency,
completeness, soundness, etc. And the invention of non-Euclidean
geometry could be traced back to Galileo.

And a German named Riemann came up with another system of geometry that also
contradicted Euclid’s first axiom: that only one line can pass through any
two points.

According to this book (which may not be the final authority on the subject
I’ll admit), Riemann’s geometry is thought to most accurately describe our
world. Oddly enough, the book is ‘Zen and the Art of Motorcycle
Maintenance’ which creates a rather strange link to another part of this
thread. Funny. Coincidence? Or not…

I bet ZAMM says there’s no such thing like coincidence…

Granted, prejudice based solely on the title may well be wrong, but it
(the title) reminds me some doubtful post-modernistic mixtures. Well,
you have explained it to me already.

ako

:wink:

Kris

“Wojtek Lerch” <> wojtek_l@yahoo.ca> > wrote in message
news:ae86qc$m9r$> 1@nntp.qnx.com> …
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.

96

“Andrzej Kocon” <ako@box43.gnet.pl> wrote in message
news:3d0cd5c0.18063641@inn.qnx.com…

On Sat, 15 Jun 2002 22:25:32 -0400, “Kris Warkentin”
kewarken@qnx.com> > wrote:
I bet ZAMM says there’s no such thing like coincidence…

Granted, prejudice based solely on the title may well be wrong, but it
(the title) reminds me some doubtful post-modernistic mixtures. Well,
you have explained it to me already.

Well, granted it’s a strange title but it makes no metaphysical claims. I
was merely being facetious [sp?]. The point is that what we see and observe
do not necessarily have much bearing on reality. Judging from some of the
more recent theory (see “The Elegant Universe” by Brian Greene) we’re quite
limited by being stuck in time at a relatively slow speed and, in fact, most
of the geometrical rules that we hold to be ‘common sense’ are merely
approximations.

cheers,

Kris

97

Kris Warkentin <kewarken@qnx.com> wrote:

“Andrzej Kocon” <> ako@box43.gnet.pl> > wrote in message
news:> 3d0cd5c0.18063641@inn.qnx.com> …
On Sat, 15 Jun 2002 22:25:32 -0400, “Kris Warkentin”
kewarken@qnx.com> > wrote:
I bet ZAMM says there’s no such thing like coincidence…

Granted, prejudice based solely on the title may well be wrong, but it
(the title) reminds me some doubtful post-modernistic mixtures. Well,
you have explained it to me already.

Well, granted it’s a strange title but it makes no metaphysical claims. I
was merely being facetious [sp?]. The point is that what we see and observe
do not necessarily have much bearing on reality. Judging from some of the
more recent theory (see “The Elegant Universe” by Brian Greene) we’re quite
limited by being stuck in time at a relatively slow speed and, in fact, most
of the geometrical rules that we hold to be ‘common sense’ are merely
approximations.

Seth Speaks would be another interesting read :slight_smile:

Cheers,
-RK

–
Robert Krten, PARSE Software Devices +1 613 599 8316.
Realtime Systems Architecture, Books, Video-based and Instructor-led
Training and Consulting at www.parse.com.
Email my initials at parse dot com.

98

Previously, Kris Warkentin wrote in qdn.cafe:

Except that Bolyai and Lobachevski showed that a proof of the fifth
postulate was impossible.

One does not usually try to prove postulates. If a postulate were provable
from other postulates, then it would be redundant.

And a German named Riemann came up with another system of geometry that also
contradicted Euclid’s first axiom: that only one line can pass through any
two points.

It doesn’t contradict Euclid, it simply exchanges his 5th postulate for
a different one.

According to this book (which may not be the final authority on the subject
I’ll admit), Riemann’s geometry is thought to most accurately describe our
world.

Yes, the universe is considered to be a 4 dimensional Riemannian manifold.
One with the metric d = SQRT(x^^2 + y^^2 + z^^2 - c^^2*t^^2). This is an
assumption of Einsteins theory of gravity.

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

99

Another coincidence: hadn’t I suppress a remark about
Riemann’s spaces and Einstein’s theory (and his complain), we would
have got two almost identical posts. The reason was that I had heard
about proposals postulating no less than 11 dimensions, so I’m quite
confused.

ako

100

Robert Krten <nospam88@parse.com> wrote:

Then, just for grins, you move the laser beams so that they are almost parallel
to each other. Then you move them further apart still. Do they suddenly cease
to intersect???

Of course!

Did you think they could gradually cease to intersect?

Whether something intersects or not is a Boolean value – if it changes,
it changes suddenly.

–
Wojtek Lerch QNX Software Systems Ltd.