The Definition of Points

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Topic:	Science > Physics
User:	"Lester Zick"
Date:	13 Mar 2007 12:52:40 PM
Object:	The Definition of Points

The Definition of Points
~v~~
In the swansong of modern math lines are composed of points. But then
we must ask how points are defined? However I seem to recollect
intersections of lines determine points. But if so then we are left to
consider the rather peculiar proposition that lines are composed of
the intersection of lines. Now I don't claim the foregoing definitions
are circular. Only that the ratio of definitional logic to conclusions
is a transcendental somewhere in the neighborhood of 3.14159 . . .
~v~~
.

User: "Hero"
Title: Re: The Definition of Points	17 Mar 2007 01:23:26 PM

On 17 Mrz., 18:49, Bob Kolker <nowh...@nowhere.com> wrote:

SucMucPaProlij wrote:

You can develop geometry based purely on real numbers and sets. You need not
assume any geometrical notions to do the thing. One of the triumphs of
mathematics in the modern era was to make geometry the child of analysis.

And it means that lines, planes and points are defined in geometry.
Make up your mind, Bob!

Not true. One of the mathematical systems which satisfy Hilbert's Axioms
for plane geometry is RxR , where R is the real number set. Points are
ordered pairs of real numbers. Not a scintilla of geometry there.

Left and right are geometrical concepts.
When You write down ( 3, 4 ) 3 is left in Your view and 4 is right.
With friendly greetings
Hero
.

User: "Bob Kolker"
Title: Re: The Definition of Points	17 Mar 2007 02:00:13 PM

Hero wrote:

Left and right are geometrical concepts.
When You write down ( 3, 4 ) 3 is left in Your view and 4 is right.

'scuse me. That could be first and second which are temporaal concepts.
The Left and Right refer to printing or writing conventions, not to
something intrinsically geometric.
Bob Kolker
.

User: "Hero"
Title: Re: The Definition of Points	17 Mar 2007 03:27:52 PM

Bob Kolker wrote:

Hero wrote:

Left and right are geometrical concepts.
When You write down ( 3, 4 ) 3 is left in Your view and 4 is right.

'scuse me. That could be first and second which are temporaal concepts.

So Hamilton, who invented calculation with these ordered pairs, was
right about his "science of pure time"?
http://www.maths.tcd.ie/pub/HistMath/People/Hamilton/PureTime/

The Left and Right refer to printing or writing conventions, not to
something intrinsically geometric.

So with Your kind of geometry You can or You can not tell, that DNA is
a right screw?
With friendly greetings
Hero
.

User: "Bob Kolker"
Title: Re: The Definition of Points	17 Mar 2007 04:13:23 PM

Hero wrote:

So with Your kind of geometry You can or You can not tell, that DNA is
a right screw?

With friendly greetings

You can tell that right and left are differnt. You can use the hand
rules to designate the orientation.
In principle one could do the Yang-Lee experiment to tell left from
right. If we communicated by radio with beings in a different part of
the normal matter universe we could (in principle) give them a procedure
for identifying left and right.
Bob Kolker
.

User: "Hero"
Title: Re: The Definition of Points	17 Mar 2007 04:39:21 PM

On 17 Mrz., 22:13, Bob Kolker <nowh...@nowhere.com> wrote:

Hero wrote:

So with Your kind of geometry You can or You can not tell, that DNA is
a right screw?

You can tell that right and left are differnt.

Can You please give me a hint, where in Your geometry or in which of
Your geometries this is axiomized or where it follows from axioms?
Or where the plane-reflection is possible?
Thanks
Hero
.

User: "Bob Kolker"
Title: Re: The Definition of Points	17 Mar 2007 04:49:59 PM

Hero wrote:

On 17 Mrz., 22:13, Bob Kolker <nowh...@nowhere.com> wrote:

Hero wrote:

So with Your kind of geometry You can or You can not tell, that DNA is
a right screw?

You can tell that right and left are differnt.

Can You please give me a hint, where in Your geometry or in which of
Your geometries this is axiomized or where it follows from axioms?
Or where the plane-reflection is possible?

On cannot transform a right spiral into a left spiral by an isometry
with a determinant of 1. By considering isometries with determinant 1
you restrict mapping that either translate or rotate or a combination.
Reflection about a line is out.
Bob Kolker
.

User: "Hero"
Title: Re: The Definition of Points	17 Mar 2007 05:09:32 PM

Hero wrote:

Left and right are geometrical concepts.
When You write down ( 3, 4 ) 3 is left in Your view and 4 is right.

Bob Kolker wrote:

'scuse me. That could be first and second which are temporaal concepts.
Hero wrote:

So Hamilton, who invented calculation with these ordered pairs, was
right about his "science of pure time"?

http://www.maths.tcd.ie/pub/HistMath/People/Hamilton/PureTime/
Bob Kolker wrote:

The Left and Right refer to printing or writing conventions, not to
something intrinsically geometric.

Hero wrote:

So with Your kind of geometry You can or You can not tell, that DNA is
a right screw?

Bob Kolker wrote:

You can tell that right and left are differnt.

Hero wrote:

Can You please give me a hint, where in Your geometry or in which of
Your geometries this is axiomized or where it follows from axioms?
Or where the plane-reflection is possible?

Bob Kolker wrote:

But in order to assign a value of minus one to a determinant ( for a
chiral change) You write it down with differing between left and right
or - again -
You refer to "first and second which are temporaal concepts".
It seems, You like dynamical geometry more than static.
With friendly greetings
Hero
PS. So far, i never saw any axioms of dynamical geometry. Anybody has
a hint?
.

User: "Tony Orlow"
Title: Re: The Definition of Points	17 Mar 2007 06:05:48 PM

Hero wrote:

On 17 Mrz., 22:13, Bob Kolker <nowh...@nowhere.com> wrote:

Hero wrote:

So with Your kind of geometry You can or You can not tell, that DNA is
a right screw?

You can tell that right and left are differnt.

Can You please give me a hint, where in Your geometry or in which of
Your geometries this is axiomized or where it follows from axioms?
Or where the plane-reflection is possible?

Thanks
Hero

A ~B<A
A A<C
Tony
.

User: "Virgil"
Title: Re: The Definition of Points	18 Mar 2007 01:28:39 AM

In article <45fc7458@news2.lightlink.com>,
Tony Orlow <tony@lightlink.com> wrote:

Hero wrote:

On 17 Mrz., 22:13, Bob Kolker <nowh...@nowhere.com> wrote:

Hero wrote:

So with Your kind of geometry You can or You can not tell, that DNA is
a right screw?

You can tell that right and left are differnt.

Can You please give me a hint, where in Your geometry or in which of
Your geometries this is axiomized or where it follows from axioms?
Or where the plane-reflection is possible?

Thanks
Hero

A ~B<A
A A<C

Which is, as usual, irrelevant.
Purely in the mathematics of three dimensional Euclidean or Cartesian
geometry, there is no way to distinguish a right handed from a left
handed system.
I understand that there is some fairly esoteric experiment in physics
which is alleged to distinguish between them.
.

User: "Bob Kolker"
Title: Re: The Definition of Points	18 Mar 2007 06:25:22 AM

Virgil wrote:

Which is, as usual, irrelevant.

Purely in the mathematics of three dimensional Euclidean or Cartesian
geometry, there is no way to distinguish a right handed from a left
handed system.

The determinent of a reflexion isometry is equal to -1.
Which tells us that right hand is not left hand, but not which is which.
Bob Kolker
.

User: "Tony Orlow"
Title: Re: The Definition of Points	18 Mar 2007 10:55:02 AM

Virgil wrote:

In article <45fc7458@news2.lightlink.com>,
Tony Orlow <tony@lightlink.com> wrote:

Hero wrote:

On 17 Mrz., 22:13, Bob Kolker <nowh...@nowhere.com> wrote:

Hero wrote:

So with Your kind of geometry You can or You can not tell, that DNA is
a right screw?

You can tell that right and left are differnt.

Can You please give me a hint, where in Your geometry or in which of
Your geometries this is axiomized or where it follows from axioms?
Or where the plane-reflection is possible?

Thanks
Hero

A ~B<A
A A<C

Which is, as usual, irrelevant.

Purely in the mathematics of three dimensional Euclidean or Cartesian
geometry, there is no way to distinguish a right handed from a left
handed system.

I understand that there is some fairly esoteric experiment in physics
which is alleged to distinguish between them.

From a mathematical point of view, it's all relative, and arbitrary,
which direction is "right" or "left". It's just a matter of transitive
asymmetric order relations. This applies to "less than" in the
quantitiative sense, as well as "proper subset". The statements above
apply to both.
.

User: "Virgil"
Title: Re: The Definition of Points	18 Mar 2007 02:01:21 PM

In article <45fd60e3@news2.lightlink.com>,
Tony Orlow <tony@lightlink.com> wrote:

Purely in the mathematics of three dimensional Euclidean or Cartesian
geometry, there is no way to distinguish a right handed from a left
handed system.

I understand that there is some fairly esoteric experiment in physics
which is alleged to distinguish between them.

TO misses the point once more!
There is no such thing as a left-handed or right-handed system in 2
dimensions, the difference between them requires 3 dimensions.
.

User: "Wolf"
Title: Re: The Definition of Points	18 Mar 2007 11:51:19 AM

Virgil wrote:

In article <45fc7458@news2.lightlink.com>,
Tony Orlow <tony@lightlink.com> wrote:

Hero wrote:

On 17 Mrz., 22:13, Bob Kolker <nowh...@nowhere.com> wrote:

Hero wrote:

So with Your kind of geometry You can or You can not tell, that DNA is
a right screw?

You can tell that right and left are differnt.

Can You please give me a hint, where in Your geometry or in which of
Your geometries this is axiomized or where it follows from axioms?
Or where the plane-reflection is possible?

Thanks
Hero

A ~B<A
A A<C

Which is, as usual, irrelevant.

Purely in the mathematics of three dimensional Euclidean or Cartesian
geometry, there is no way to distinguish a right handed from a left
handed system.

I understand that there is some fairly esoteric experiment in physics
which is alleged to distinguish between them.

The experiment merely shows that there are in fact left- and right-
handed thingummies. It does not tell you which is which. "Right" and
"left" are, as VK pointed out, purely arbitrary terms. We learn early on
which word to use for which hand, and as observation and experience
show, it ain't easy to learn arbitrary terms.
It was once explained to me that the right hand is the one with the
thumb on the left, and the left hand is the one with the thumb on the right.
Which nicely sums um VK's point. ;-)
--
Wolf
"Don't believe everything you think." (Maxine)
.

User: "Hero"
Title: Re: The Definition of Points	18 Mar 2007 04:05:49 AM

Tony Orlow wrote:

Hero wrote:

Bob Kolker wrote:

Hero wrote:

So with Your kind of geometry You can or You can not tell, that DNA is
a right screw?

You can tell that right and left are differnt.

Can You please give me a hint, where in Your geometry or in which of
Your geometries this is axiomized or where it follows from axioms?
Or where the plane-reflection is possible?

Thanks
Hero

A ~B<A
A A<C

This is written in a math language foreign to me.
~ means NOT
-> means Material Implication
^ means AND
< means ? ( 3 < 4 is three is smaller than 4)
( the only modell to Your two statements i did find:
A; B, C natural numbers, ~ means minus/negative)
With friendly greetings
Hero
.

User: "Tony Orlow"
Title: Re: The Definition of Points	18 Mar 2007 11:01:32 AM

Hero wrote:

Tony Orlow wrote:

Hero wrote:

Bob Kolker wrote:

Hero wrote:

So with Your kind of geometry You can or You can not tell, that DNA is
a right screw?

You can tell that right and left are differnt.

Can You please give me a hint, where in Your geometry or in which of
Your geometries this is axiomized or where it follows from axioms?
Or where the plane-reflection is possible?
Thanks
Hero

A ~B<A
A A<C

Hi Hero -
'~' indeed means logical "not". '<' means "less than", and can be
interpreted in a number of ways, such as "is to the left of", "is a
smaller quantity than", or "is a proper subset of". You may be able to
think of other examples of transitive and asymmetric relations, such as
"is inferior to".
:)
Tony
.

User: "Hero"
Title: Re: The Definition of Points	18 Mar 2007 01:23:28 PM

Tony Orlow wrote:

Hero wrote:

Tony Orlow wrote:

Hero wrote:

Bob Kolker wrote:

Hero wrote:

So with Your kind of geometry You can or You can not tell, that DNA is
a right screw?

You can tell that right and left are differnt.

Can You please give me a hint, where in Your geometry or in which of
Your geometries this is axiomized or where it follows from axioms?
Or where the plane-reflection is possible?

A ~B<A
A A<C

Hi Hero -

'~' indeed means logical "not". '<' means "less than", and can be
interpreted in a number of ways, such as "is to the left of", "is a
smaller quantity than", or "is a proper subset of". You may be able to
think of other examples of transitive and asymmetric relations, such as
"is inferior to".

:)

I didn't know, that A ~B<A means A ~ ( B<A ).
But how does this fit to left and right screws and to reflection?
It's more like :) and :(
A reflection is an involution, half of an identity, so to speak:
r ( r ( A ) ) = A
And a right screw is a form, the form of DNA.
Join the four points of a tetra in a consecutive way with three lines,
You have one type of screw. And the other three edges are of the
opposite type. Still more basic is a skew tetra and it's reflection,
they are different to each other, chiral, but without further
differences one can not say which is left-type and which is right-
type.
One abstract example is a cartesian coordinate system, more abstract a
vector-space of three dimensions with a cross-product of vectors:
x cross y = z, and the other: x cross z = y.
So who of the modern math axiomatists ( Hilbert, Tarski..) of geometry
treat this subject?
With friendly greetings
Hero
PS I was able to think of such relations as " is inferior to". If i
would be inferior to You, i would be more down to earth and Your nose
would be higher up. :)
.

User: "Tony Orlow"
Title: Re: The Definition of Points	18 Mar 2007 02:59:38 PM

Hero wrote:

Tony Orlow wrote:

Hero wrote:

Tony Orlow wrote:

Hero wrote:

Bob Kolker wrote:

Hero wrote:

So with Your kind of geometry You can or You can not tell, that DNA is
a right screw?

You can tell that right and left are differnt.

Can You please give me a hint, where in Your geometry or in which of
Your geometries this is axiomized or where it follows from axioms?
Or where the plane-reflection is possible?

A ~B<A
A A<C

Hi Hero -

'~' indeed means logical "not". '<' means "less than", and can be
interpreted in a number of ways, such as "is to the left of", "is a
smaller quantity than", or "is a proper subset of". You may be able to
think of other examples of transitive and asymmetric relations, such as
"is inferior to".

:)

I didn't know, that A ~B<A means A ~ ( B<A ).

Sorry, I thought it was clear, with A and B numbers, that the negation
'~' pertained to the statement "B<A". That's what I meant.

But how does this fit to left and right screws and to reflection?
It's more like :) and :(

Ummm, it doesn't really. I brought it up to answer the original inquiry,
as I saw it, where "right and left" were suggested as interpretations of
'>' and '<'. As far as I'm concerned, they're interchangeable.

A reflection is an involution, half of an identity, so to speak:
r ( r ( A ) ) = A
And a right screw is a form, the form of DNA.
Join the four points of a tetra in a consecutive way with three lines,
You have one type of screw. And the other three edges are of the
opposite type. Still more basic is a skew tetra and it's reflection,
they are different to each other, chiral, but without further
differences one can not say which is left-type and which is right-
type.
One abstract example is a cartesian coordinate system, more abstract a
vector-space of three dimensions with a cross-product of vectors:
x cross y = z, and the other: x cross z = y.
So who of the modern math axiomatists ( Hilbert, Tarski..) of geometry
treat this subject?

With friendly greetings
Hero
PS I was able to think of such relations as " is inferior to". If i
would be inferior to You, i would be more down to earth and Your nose
would be higher up. :)

I suppose. I didn't mean anything personal, of course. :)
.

User: "hagman"
Title: Re: The Definition of Points	19 Mar 2007 04:22:26 PM

On 17 Mrz., 19:23, "Hero" <Hero.van.Jind...@gmx.de> wrote:

On 17 Mrz., 18:49, Bob Kolker <nowh...@nowhere.com> wrote:> SucMucPaProlij wrote:

And it means that lines, planes and points are defined in geometry.
Make up your mind, Bob!

Left and right are geometrical concepts.
When You write down ( 3, 4 ) 3 is left in Your view and 4 is right.

With friendly greetings
Hero

No, (3,4) is {{3},{3,4}} and then 3 is the only element of the only
singleton element and 4 is the other guy.
.

User: "Hero"
Title: Re: The Definition of Points	19 Mar 2007 04:55:19 PM

hagman wrote:

Hero wrote:

Bob Kolker wrote:

...Points are ordered pairs of real numbers. Not a scintilla of geometry there.

Left and right are geometrical concepts.
When You write down ( 3, 4 ) 3 is left in Your view and 4 is right.

No, (3,4) is {{3},{3,4}} and then 3 is the only element of the only
singleton element and 4 is the other guy.

Congratulations, You win.
With friendly greetings
Hero
.

User: "VK"
Title: Re: The Definition of Points	17 Mar 2007 04:29:39 PM

On Mar 17, 9:23 pm, "Hero" <Hero.van.Jind...@gmx.de> wrote:

Left and right are geometrical concepts.

Oh, that's ingenious! I was just lurking around, but it's so really
awesome as a statement for a linguist - I couldn't resist.
So "left and right are geometrical concepts". Good, so you don't mind
to play an old game with me? The imaginary concept of left and right
was once used in one sci-fi story, so I keep close to it for the
simplicity:
I'm an E.T. from another planet inside of a perfectly symmetrical
cabin. There is only door behind me and in front of me - symmetrical
against the door - there are two buttons. Left side button is broken
and will explode the cabin. Right side button will send me back to my
planet. Alas the words "left" and "right" are not known to me. Your
task is by using radio (but no video communication) to instruct me to
press the right (in both sense) button. I'm very smart and can draw
whatever you will tell me, I just don't know what the hey "left" and
"right" is. Care to try to send me to my planet?
.

User: "SucMucPaProlij"
Title: Re: The Definition of Points	17 Mar 2007 04:59:09 PM

"VK" <schools_ring@yahoo.com> wrote in message
news:1174166979.646294.96500@e1g2000hsg.googlegroups.com...

On Mar 17, 9:23 pm, "Hero" <Hero.van.Jind...@gmx.de> wrote:

Left and right are geometrical concepts.

Oh, that's ingenious! I was just lurking around, but it's so really
awesome as a statement for a linguist - I couldn't resist.

So "left and right are geometrical concepts". Good, so you don't mind
to play an old game with me? The imaginary concept of left and right
was once used in one sci-fi story, so I keep close to it for the
simplicity:

I'm an E.T. from another planet inside of a perfectly symmetrical
cabin. There is only door behind me and in front of me - symmetrical
against the door - there are two buttons. Left side button is broken
and will explode the cabin. Right side button will send me back to my
planet. Alas the words "left" and "right" are not known to me. Your
task is by using radio (but no video communication) to instruct me to
press the right (in both sense) button. I'm very smart and can draw
whatever you will tell me, I just don't know what the hey "left" and
"right" is. Care to try to send me to my planet?

Cabin is symetrical and you can't distinguish between left and right.
When you say "Left button is broken" question is "what left button?"
There is no left or right half of circle.
.

User: ""
Title: Re: The Definition of Points	17 Mar 2007 05:38:30 PM

In article <1174170793.549628.45350@b75g2000hsg.googlegroups.com>, "VK" <schools_ring@yahoo.com> writes:

On Mar 18, 12:59 am, "SucMucPaProlij" <mrjohnpauldike2...@hotmail.com>
wrote:

Cabin is symetrical and you can't distinguish between left and right.
When you say "Left button is broken" question is "what left button?"
There is no left or right half of circle.

Why do you think that there is ***anything*** in calculus that depends
on whether you use base 3, 10, 42 or whatever?
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
.

User: "Lester Zick"
Title: Re: The Definition of Points	18 Mar 2007 02:10:12 PM

On Sat, 17 Mar 2007 22:38:30 GMT,

wrote:

In article <1174170793.549628.45350@b75g2000hsg.googlegroups.com>, "VK" <schools_ring@yahoo.com> writes:

On Mar 18, 12:59 am, "SucMucPaProlij" <mrjohnpauldike2...@hotmail.com>
wrote:

Cabin is symetrical and you can't distinguish between left and right.
When you say "Left button is broken" question is "what left button?"
There is no left or right half of circle.

Why do you think that there is ***anything*** in calculus that depends
on whether you use base 3, 10, 42 or whatever?

Good question.
~v~~
.

User: "VK"
Title: Re: The Definition of Points	17 Mar 2007 05:33:13 PM

On Mar 18, 12:59 am, "SucMucPaProlij" <mrjohnpauldike2...@hotmail.com>
wrote:

Cabin is symetrical and you can't distinguish between left and right.
When you say "Left button is broken" question is "what left button?"
There is no left or right half of circle.

Yep, this is what I mean. That was to argue with the Hero's statement
that "left and right are geometrical concepts". Left and right are
semantical concepts appeared grace to the particular human body
symmetry. If octopuses got the intellect, I would die to see their
geometry books. And I would sell my new car for any junior-high
calculus book from a planet populated by creatures having three pods
instead of ten fingers - so they are naturally using base-3 numeral
system with base-10 system being a scientific domain obscurity. The
latter dream gets us OT though. So anyone is still willing to send
poor ET back home? Unlimited chalk reserves, he/she/it ready to draw
whatever instructed on the floor and on the wall, the cabin is square
or cylinder - whatever one likes. In the sci-fi story - after having
realized the geometry failure for the matter they just told him to
press whatever button look more "warm". Other word the problem was
solved by purely "good luck means".
I don't know how Yang-Lee's violation of parity would help in a
geometrical task, but my knowledge of the referred entity is highly
limited.
.

User: "SucMucPaProlij"
Title: Re: The Definition of Points	18 Mar 2007 12:12:13 PM

I'm an E.T. from another planet inside of a perfectly symmetrical
cabin. There is only door behind me and in front of me - symmetrical
against the door - there are two buttons. Left side button is broken
and will explode the cabin. Right side button will send me back to my
planet. Alas the words "left" and "right" are not known to me. Your
task is by using radio (but no video communication) to instruct me to
press the right (in both sense) button. I'm very smart and can draw
whatever you will tell me, I just don't know what the hey "left" and
"right" is. Care to try to send me to my planet?

You can tell him to flush a toilette. Water in toilette will spin in one
direction. Maybe this can help. I just want him to live!
.

User: "Bob Kolker"
Title: Re: The Definition of Points	17 Mar 2007 04:32:46 PM

VK wrote:>

Send a lengthy radio communication of Yang-Lee's violation of parity
hypothesis along with Madame Wu's experiment to verify it.
The ET will probably die of old age, but, in principle, this could work.
Bob Kolker
.

User: "Lester Zick"
Title: Re: The Definition of Points	17 Mar 2007 06:34:55 PM

On Sat, 17 Mar 2007 12:03:44 -0400, Bob Kolker <nowhere@nowhere.com>
wrote:

Tony Orlow wrote:

Yes, the relationship between points and lines is rather codependent,
isn't it? I looked at some of the responses, and indeed, one can define
points as tuples of coordinates, but of course, that all depends on
defining a set of dimensions as a space to begin with, each dimension
constituting an infinite line along which that coordinate is defined. In
language, both points and lines are taken as primitives, since their
properties are not rooted in symbols and strings, but geometry. So, we
may be left with the question as to what the primitives of geometry
really are, sets of points, or sequences of lines. That's the conundrum
right, that differences and differences between differences are lines,
and not points? :)

You can develop geometry based purely on real numbers and sets. You need
not assume any geometrical notions to do the thing. One of the triumphs
of mathematics in the modern era was to make geometry the child of analysis.

So you can develop geometry without assuming any geometrical notions?
I don't see any evidence modern math has managed to any thing of the
kind.
~v~~
.

User: "Lester Zick"
Title: Re: The Definition of Points	13 Mar 2007 04:44:09 PM

On 13 Mar 2007 11:20:47 -0700, "Ross A. Finlayson"
<raf@tiki-lounge.com> wrote:

Lester Zick wrote:

The Definition of Points
~v~~

In the swansong of modern math lines are composed of points. But then
we must ask how points are defined? However I seem to recollect
intersections of lines determine points. But if so then we are left to
consider the rather peculiar proposition that lines are composed of
the intersection of lines. Now I don't claim the foregoing definitions
are circular. Only that the ratio of definitional logic to conclusions
is a transcendental somewhere in the neighborhood of 3.14159 . . .

~v~~

You should ask me.

Why?
~v~~
.

User: "Math1723"
Title: Re: The Definition of Points	17 Mar 2007 03:15:42 PM

On Mar 13, 5:44 pm, Lester Zick <dontbot...@nowhere.net> wrote:

On 13 Mar 2007 11:20:47 -0700, "Ross A.Finlayson"

You should ask me.

Why?

Perhaps he could use a good laugh?
.

User: "Lester Zick"
Title: Re: The Definition of Points	18 Mar 2007 12:33:59 PM

On 17 Mar 2007 13:15:42 -0700, "Math1723" <anonym1723@aol.com> wrote:

On Mar 13, 5:44 pm, Lester Zick <dontbot...@nowhere.net> wrote:

On 13 Mar 2007 11:20:47 -0700, "Ross A.Finlayson"

You should ask me.

Why?

Perhaps he could use a good laugh?

I'm sure we all could. Is that it?
~v~~
.

User: "hagman"
Title: Re: The Definition of Points	16 Mar 2007 09:00:02 AM

On 13 Mrz., 18:52, Lester Zick <dontbot...@nowhere.net> wrote:

The Definition of Points
~v~~

In the swansong of modern math lines are composed of points. But then
we must ask how points are defined? However I seem to recollect
intersections of lines determine points. But if so then we are left to
consider the rather peculiar proposition that lines are composed of
the intersection of lines. Now I don't claim the foregoing definitions
are circular. Only that the ratio of definitional logic to conclusions
is a transcendental somewhere in the neighborhood of 3.14159 . . .

~v~~

Please look up the difference between "define" and "determine".
In a theory that deals with "points" and "lines" (these are typically
theories about geometry), it is usual to leave these terms themselves
undefined
and to investigate an incidence relation "P on L" (for points P and
lines L)
with certain properties
Then the intersection of two lines /determines/ a point in the sense
that
IF we have two lines L1 and L2
AND there exists a point P such that both P on L1 and P on L2
THEN this point is unique.
This is usually stated as an axiom.
And it does not define points nor lines.
.

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