What do the axes of coordinates show?
V.Gopal
The origin is (0,0). Every number on X-coordinate gives its distance
from the origin or from zero. Thus in geometry a number on the axis
directly gives its distance from the origin or from 0. When number
directly gives distance from 0 then the problem is to find how far
should we place 1 (unit) from 0. If X is a point on X-axis and the
number marked on the point A is 'x', then length OX/x = 1. Although OX
(distance from origin) and x (the number on the point X) are variables
OX/x is always 1. If we decide to place 1 at a distance of, say, 1"
from the origin, then the 'distance' OX is not 'continuos' because the
number of 1s given by OX/x must be infinite if OX is compact and
continuous. If number of points within 1 is infinite then we can never
reach 0 or the origin from 1. (Zeno's paradox. 1=1/2+ 1/2^2 + 1/2^3
-------- has infinite terms.) I wish to know in geometry whether
OX/x=1 or not. If OX/x = 1 also OX is continuous, then it means OX/x=1
then we can never know how far is 1 from 0 and every finite length is
1. If we want numbers on the axes of coordinates then we have to use a
finite unit of length to mark the numbers and fractions would serve
the same purpose as unit. In geometry numbers more than 1 do not have
reciprocals!
Uncle Al
>
> The co-ordinates of a point, that is, (x,y) are always pure numbers.
> The origin is (0,0).
Wrong. Confocal ellipsoidal coordinates, moron.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!
Ken Pledger
vgop...@rediffmail.com (V.Gopal) wrote:
> The co-ordinates of a point, that is, (x,y) are always pure numbers.
> .... Thus in geometry a number on the axis directly gives its distance
> from the origin .... then the problem is to find how far should we place
> 1 (unit) from 0.
It doesn't seem entirely clear where you're starting.
If you start with a Euclidean plane and then put a coordinate system
on it, you can choose any two perpendicular lines as axes, and any point
(except the origin) on the x axis as (1,0). Once you've chosen those
things, you don't change them. Then it's possible to set up coordinates
(x,y) for every point in the plane.
OTOH if you start with just the real numbers, you can define points
to _be_ ordered pairs (x,y), and then introduce suitable Euclidean notions
of length, angle, etc.
> .... If we decide to place 1 at a distance of, say, 1" from the origin,
> then ....
This mention of inches suggests that you're mixing mathematics with
physics. Certainly we draw graphs on paper using physical lengths, for
two reasons. One is to apply our geometrical theory to the real world.
The other (which seems closer to your concerns) is to aid our imaginations
in thinking about the abstractly defined Cartesian plane. However, the
pure theory can't involve any physical unit of length.
I hope these comments will at least help clear up some
misunderstandings and perhaps clarify your question.
Ken Pledger.
Bob Pease
"Ken Pledger" <Ken.P...@vuw.ac.nz> wrote in message
news:Ken.Pledger-29...@pascal.mcs.vuw.ac.nz...
Don't hold your breath about this poster making anything clear.
Check Google groups for previous attempts by other posters to communicate
with him.
RJ Pease
andi babian
Sounds like my kind of place :)
agb
Ronald Stepp
news:3DBE7D03...@cruzio.com...
> Is this where the hyper-intelligent come to heap abuse on the ignorant?
> Sounds like my kind of place :)
Ignorance is not bad. Intentionally posting crap when you are not ignorant
IS bad.
Bob Pease
> Sounds like my kind of place :)
> agb
In general the folks on this ng seem to be pretty tolerant.
Especially of homework nerds.
I like to see good homework stuff bandied about if it is clear that the
poster has tried something and just doesn't want answers to copy and hand
in.
One of the best examples was where a MAT108 problem was answered at a MAT
500+ level.
I hope the dork handed it in that way!!
On occasion dorkiness flounders about, and so I still have to use the
Plonquer at times.
RJ Pease
Spaceman
>If number of points within 1 is infinite then we can never
>reach 0 or the origin from 1. (Zeno's paradox. 1=1/2+ 1/2^2 + 1/2^3
>-------- has infinite terms.)
Zeno is a math moron.
The number of points in between 0 and 1 ARE infinite.
a 1 is an abstract
abstracts in math can be "increased"
to produce more interal points... INFINITELY!
(technology is the only limit proven so far)
otherwise,
the techology has the only limits.
not the points in between 0 and 1.
1 Planck/2= What?
simple.
1/2 Plancks length.
no limit to "devision"
only to technology that can devide it (the saw blade)
:)
Zeno, and Planck,
are morons.
Today,
we should be laughing at them and thanking them for
making so many fools in the world.
:)
If your blade is only one Planck length.
(the smallest wood piece you can work with must be slightly larger)
:)
too simple huh?
:)
Hint,
There are 1 million Driscoll Spaces inside a Planck length.
:)
and.
There are a few trillion distances inside 1 Driscoll Space.
:)
and Basic math proves it.
Very simply.
:)
James M Driscoll Jr
Spaceman
http://www.realspaceman.com
Gregory L. Hansen
V.Gopal <vgop...@rediffmail.com> wrote:
>The co-ordinates of a point, that is, (x,y) are always pure numbers.
>The origin is (0,0). Every number on X-coordinate gives its distance
>from the origin or from zero. Thus in geometry a number on the axis
>directly gives its distance from the origin or from 0. When number
>directly gives distance from 0 then the problem is to find how far
>should we place 1 (unit) from 0. If X is a point on X-axis and the
1/10 inch, according to the little squares on my graph paper.
Put it wherever you like, and wherever you put it will define a unit
distance.
>number marked on the point A is 'x', then length OX/x = 1. Although OX
>(distance from origin) and x (the number on the point X) are variables
>OX/x is always 1. If we decide to place 1 at a distance of, say, 1"
>from the origin, then the 'distance' OX is not 'continuos' because the
>number of 1s given by OX/x must be infinite if OX is compact and
>continuous. If number of points within 1 is infinite then we can never
>reach 0 or the origin from 1. (Zeno's paradox. 1=1/2+ 1/2^2 + 1/2^3
>-------- has infinite terms.) I wish to know in geometry whether
For some reason, Zeno chose to approach his destination taking smaller and
smaller steps in each time interval. It works better if you just keep
walking, 1+1+1+1...
--
"A nice adaptation of conditions will make almost any hypothesis agree
with the phenomena. This will please the imagination but does not advance
our knowledge." -- J. Black, 1803.
Randy Poe
> Is this where the hyper-intelligent come to heap abuse on the ignorant?
> Sounds like my kind of place :)
No. It's where those of any intelligence come to heap abuse
on those who think that ignorance of physics makes them
physics experts, and anybody who doesn't think so is
closed minded and a slavish unthinking lapdog of the
orthodoxy.
- Randy
TB
>>From: vgop...@rediffmail.com (V.Gopal)
>
>
>>If number of points within 1 is infinite then we can never
>>reach 0 or the origin from 1. (Zeno's paradox. 1=1/2+ 1/2^2 + 1/2^3
>>-------- has infinite terms.)
>
>
> Zeno is a math moron.
> The number of points in between 0 and 1 ARE infinite.
> a 1 is an abstract
> abstracts in math can be "increased"
> to produce more interal points... INFINITELY!
Spaceman is lost in abstract math... Where are the REALs, James?
Can you keep dividing a pile of 64 tires in half forever and still have
tires? Apples? Beans? Hmmm...????
You can't, on one hand, tell us that math without REAL objects is bullshit
and base your conclusion that negative numbers don't exist thereon yet, on
the other hand, use pure math here to claim that something is *physically*
true (ability to infinitely divide an object in half).
>
> Zeno, and Planck,
> are morons.
> Today,
> we should be laughing at them and thanking them for
> making so many fools in the world.
> :)
Jos, (insert gratuitous comma) and Spacegoof, (another gratuitous comma)
are morons.
Today, (yet another gratuitious comma)
we *are* laughing at them and thanking them for
entertaining so many of us in the world.
:)
>
> If your blade is only one Planck length.
> (the smallest wood piece you can work with must be slightly larger)
> :)
>
> too simple huh?
> :)
>
> Hint,
> There are 1 million Driscoll Spaces inside a Planck length.
> :)
Hint,
a "Driscoll Space" is the unit volume of the "Driscoll Intellect." Since
it's well known that the latter is zero then the former can also be zero.
Therefore there can be an *infinite* number of "Driscoll Spaces" inside the
dimensions of a Planck length.
> and.
> There are a few trillion distances inside 1 Driscoll Space.
> :)
> and Basic math proves it.
> Very simply.
> :)
Basic math proves that (-x) * (-x) = (+x) * (+x), and proves it very simply
too!
:)
-- TB
Thad Coons
news:apmc87$dk0$1...@rainier.uits.indiana.edu...
> In article <38af3945.02102...@posting.google.com>,
> V.Gopal <vgop...@rediffmail.com> wrote:
> >The co-ordinates of a point, that is, (x,y) are always pure numbers.
> >The origin is (0,0). Every number on X-coordinate gives its distance
> >from the origin or from zero. Thus in geometry a number on the axis
> >directly gives its distance from the origin or from 0. When number
> >directly gives distance from 0 then the problem is to find how far
> >should we place 1 (unit) from 0. If X is a point on X-axis and the
>
> 1/10 inch, according to the little squares on my graph paper.
>
> Put it wherever you like, and wherever you put it will define a unit
> distance.
>
> >number marked on the point A is 'x', then length OX/x = 1. Although OX
> >(distance from origin) and x (the number on the point X) are variables
> >OX/x is always 1. If we decide to place 1 at a distance of, say, 1"
> >from the origin, then the 'distance' OX is not 'continuos' because the
> >number of 1s given by OX/x must be infinite if OX is compact and
> >continuous. If number of points within 1 is infinite then we can never
> >reach 0 or the origin from 1. (Zeno's paradox. 1=1/2+ 1/2^2 + 1/2^3
> >-------- has infinite terms.) I wish to know in geometry whether
>
> For some reason, Zeno chose to approach his destination taking smaller and
> smaller steps in each time interval. It works better if you just keep
> walking, 1+1+1+1...
> --
It even works if you divide the time intervals as well as the steps in half,
but it doesn't look like that idea occurred to Zeno either...
Thad Coons
V.Gopal
second. It meas that along every axis of coordinate we assume that
either length/length is constant or length/time is constant. Therefore
we assume that along every axis of coordinate TanA is constant. please
let me know if I am wrong.
May the noble minded scholars instead of cherishing ill-will kindly
correct any error here committed through dullness of intellect in the
way of wrong statements and interpretations.
Ken Pledger
> ....
> Along an axis of coordinate we assume that 1"=100 feet or 1"= 1
> second. It meas that along every axis of coordinate we assume that
> either length/length is constant or length/time is constant. Therefore
> we assume that along every axis of coordinate TanA is constant....
Now here you're definitely mixing mathematics with physics. The
expression tan(A) always represents a pure number, never anything like
"one second per inch". I find it helpful always to keep absolutely clear
when I'm thinking of mathematical objects which are entirely in the mind,
and when I'm applying them to physical objects such as graphs on paper
using units of distance, time, etc.
Ken Pledger.
V.Gopal
that give level. The number that gives level is like ordinal numbers
and ordinal numbers are exactly like TanA. Although angle A is also
like ordinal numbers A returns to its starting point after 360
degrees. Since ordinal numbers are endless we have to represent
ordinal numbers by TanA. The Ordinal numbers are also like
frequencies, therefore any discussion on pure numbers seems to be a
discussion on physics. If axes of coordinates only show 'consistent
quantities' then in geometry we would only get straight lines. In
geometry ordinal numbers enter because geometry also gives position of
every number. Therefore in geometry 0 occupies ONE point and 10^-100
also occupies ONE point and 1, 10 etc also occupy ONE point (this is
how we get hyperbola). It is strange that sometimes we assume that all
points are of the same size (in hyperbola) and some times we assume as
the number decreases the size of the point also decreases. In A vs
TanA curve although we are showing all numbers from 0 to 1, space
occupied by each point depends on the value of TanA. It seems that,
when every ordinal number, irrespective of its 'value' occupy same
amount of space then then line shows a^x (where a<1), where a is the
space between two consecutive values of a^x. When the space occupied
by each ordinal number is equal to its value then it is equivalent to
X^X where X approaches from 1 to 0. We must remember that ordinal
number is TanA and unless TanA or slope 'm' is a comtinuous variable
we cannot get a curve. In geometry we are compelled to show that a
number X and its reciprocal 1/X both begin to increase from 0 (zero)
and X and 1/X occupy the same point whatever be the value of X. Does
it mean that in geometry numbers do not have their reciprocals?
Barb Knox
vgop...@rediffmail.com (V.Gopal) wrote:
> Ken.P...@vuw.ac.nz (Ken Pledger) wrote in message
news:<Ken.Pledger-30...@pascal.mcs.vuw.ac.nz>...
> > In article <38af3945.02102...@posting.google.com>,
> > vgop...@rediffmail.com (V.Gopal) wrote:
> >
> > > ....
> > > Along an axis of coordinate we assume that 1"=100 feet or 1"= 1
> > > second. It meas that along every axis of coordinate we assume that
> > > either length/length is constant or length/time is constant. Therefore
> > > we assume that along every axis of coordinate TanA is constant....
> >
> > Now here you're definitely mixing mathematics with physics. The
> > expression tan(A) always represents a pure number, never anything like
> > "one second per inch". I find it helpful always to keep absolutely clear
> > when I'm thinking of mathematical objects which are entirely in the mind,
> > and when I'm applying them to physical objects such as graphs on paper
> > using units of distance, time, etc.
> >
> > Ken Pledger.
> Pure numbers
As opposed to "impure" numbers? An example of each would be helpful.
> are of two types - one that gives quantity and the other that give level.
Huh? Some examples of "quantity" and "level" would be very helpful.
> The number that gives level is like ordinal numbers
By "exactly like" do you mean isomorphic? Are you saying that "quantity"
v. "level" numbers is the same distinction as cardinals v. ordinals? If
so, why not just use the standard the terminology? If not, what ARE you
saying?
> and ordinal numbers are exactly like TanA.
Rubbish. You really do need to give an example here.
> Although angle A is also
> like ordinal numbers A returns to its starting point after 360
> degrees.
And tan(A) doesn't?!?
> Since ordinal numbers are endless
Are you talking about transfinite ordinals here? If not, what ARE you
talking about?
> we have to represent ordinal numbers by TanA.
Utter rubbish. What is your proposed mapping between the (countable)
ordinals and the (uncountable) values of tan(A)?
> The Ordinal numbers are also like frequencies,
With sufficient imagination a raven is also like a writing desk. In WHAT
SENSE are they "like"?
> therefore any discussion on pure numbers seems to be a
> discussion on physics.
That depends on the seemer. I would give you long odds that for almost
all the readers of these posts, "pure" numbers (whatever exactly you might
mean by that) and ordinal numbers seem nothing at all like physics.
> If axes of coordinates only show 'consistent quantities'
Is this a technical term, or just more rubbish?
> then in geometry we would only get straight lines.
How so?
> In geometry ordinal numbers enter because geometry also gives position
> of every number.
If you are referring to Euclidean co-ordinate geometry then positions are
represented by reals, not by ordinals. What (if anything) ARE you
referring to?
> Therefore in geometry 0 occupies ONE point and 10^-100
> also occupies ONE point and 1, 10 etc also occupy ONE point
At last, something I agree with (assuming we are restricted to
1-dimensional co-ordinate geometry, which is a rather uninteresting
beast).
> (this is how we get hyperbola).
Say WHAT?!? Please provide the intermediate steps between the real number
line (your "points") and hyperbolae.
> It is strange that sometimes we assume that all
> points are of the same size (in hyperbola)
What do you mean by the "size" of a point, and what does that have to do
with hyperbolae?
> and some times we assume as
> the number decreases the size of the point also decreases.
What is "the number" here, and for goodness sake what sort of non-standard
geometry are you using where "points" not only have a non-zero "size", but
that size VARIES?
> In A vs
> TanA curve although we are showing all numbers from 0 to 1, space
> occupied by each point depends on the value of TanA.
It sure looks like you are trying to use ordinary Euclidean co-ordinate
geometry here. But you are failing miserably. In ordinary Euclidean
co-ordinate geometry, "each point" occupies exactly NO space. Got that?
NO space. None. Nil. Nichts. Nada.
[further flatulence snipped]
You post a fair bit here, and to me (and others) it all seems like
rubbish. You do seem to be trying to make some point, but (1) it is
thorougly unclear what that point is, and (2) your half-assed use of
mathematics certainly fails to make any point whatsoever.
Please, WITHOUT attempting to use mathematical analogies, tell us the
point you are trying to make.
--
---------------------------
| BBB b \ barbara minus knox at iname stop com
| B B aa rrr b |
| BBB a a r bbb |
| B B a a r b b |
| BBB aa a r bbb |
-----------------------------
MasterCougar
posted news:20021029103634...@mb-mq.aol.com:
> Zeno is a math moron.
>
This coming from the math moron who thinks that -4 * -4 = -16. Stupid
fuck, go to a real school and get educated.
--
Marc,
This is where I would normally put a funny sig, but now I just don't have
it in me.
Spaceman
> This coming from the math moron who thinks that -4 * -4 = -16. Stupid
>fuck, go to a real school and get educated.
>
Dear Master Nobody,
as long as multiplying a flat eastern direction will get me further east.
I laugh at you!
<ROFLOL>
you would flatten your nose on the windshield during the
"direction change for no reason"
<ROFLOL>
You are the stupid one.
Never worked on anything real in your life yet huh?
poor kid.
<LOL>
kal
> It is strange that sometimes we assume that all
> points are of the same size (in hyperbola) and
> some times we assume as the number decreases the
> size of the point also decreases.
<snip>
"A point is that which has no part."
-- Euclid, Elemetns: Book I Definition 1
I don't know what you are drinking but you should
patent that stuff.
As for the Zeno's paradox stuff, it's Physics and
not mathematics. To paraphrase Bertrand Russel:
"Zeno made an implicit assumption that A MOVING
BODY IS IN A STATE OF MOTION. This is now known
to be wrong."
As for the "axes of co-ordinates": a co-ordinate
system and its physical representation are two
different things.
It is customery and useful to use 'real lines' for
the axes (of say a Cartesian co-ordinate system.)
But you can assign numbers to points on the line
in any way that satisfies your purpose or fancy.
It is not necessary that the physical distance
between 0 and 1 should be the same as that between
1 and 2.
You can, for example, define the PHYSICAL
representation of a real line such that the
distance between points denoted by integers
halves as one moves away from point 0.
Perhaps this may not be very useful in real world
applications but as a representations this is
just as valid as any other scheme.
So, in effect, a "real line" need not be physically
unbounded in length.
V.Gopal
My answers to your questions:
'Pure numbers' are numbers without units of measurement. In
[2](inches) 2 is a pure number. we can write 2"= 1/6 foot. 2 is not
equal to 1/6 in pure maths but here it is. In pur mathematics number
gives 'quantity' without unis. I used the word 'quantity' to remind
that if you remove 1 from 100 you cannot know which one you have
picked up. First number 1 or any number from in between.
Level is given by ordinal number. 1st. 2nd. 3rd --- 100th are ordinal
numbers.
If you remove any one number from a series of ordinal numbers the gap
is not filled by the preceding or the succeeding number; the gao
remains, you cannot use ordinal numbers in any calculations.
You can use any terminology to indicate these two types of numbers.
The word 'quantity' immediately tells that a number has no particular
position in a quantity.
Ordinal number give 'potential difference' therefore all 'point
functions' are ordinal numbers. You cannot add pressures,
temperatures, frequencies, velocities etc. Since we cannot add ordinal
numbers, only a 'physical process' can change the ordinal number.
Angle A increases from 0 to 360 degrees and returns to the same
POSITION.
Tan A increases from 0 to any number as big as you can imagine and
never returns to 0 again.
There are as many ordinal numbers as there are cardinal numbers. I use
the term 'quantity' because we cannot know how many 'cardinal numbers'
or units are there within 1.
If the divisions on the axes of coordintes are equally spaced then it
means we are using a homogeneous and cosistent unit of measurement.
if both the axes of coordinates are marked by homogeneous or
consistent units. that is if the 'scales' on the axes are fixed then
we can only get straight line. Certain things cannot be explained you
have feel it.
Thanks God, you accept that 0, 10^-100, 1, 10 all occupy one point
each. Then, when can we reach 0 from 1. In fact we never reach 0 or
1nfinity in a hyperbola. Unless 0 occupies no space and each 'number'
in its own position occupies only as much space as its distance
distance from 0 we can never reach 0 from 1. On Y=mX+c there is only
one number equal to 'm' and at every point on the line it occupies the
same space.
Some body has insisted that a point does not occupy any space. If X
and Y coordinates do not occupy any space then how can we imagine a
curve to 'exist'?
The purpose of this post is to prove that geometry is dimensionless if
the lines are supposed to be continuous and the moment numbers enter
in geometry all lines becomes discontinuous. Continuous lines require
continuous change in length. What it means is beyond the scope of
present discussion.
May the noble minded scholars correct the errors here committed
through dullness of intellect.
MasterCougar
(Spaceman) posted news:20021030173317...@mb-fp.aol.com:
> Dear Master Nobody,
> as long as multiplying a flat eastern direction will get me further
east.
> I laugh at you!
>
That's because you are too fucking stupid to realize that you are
MISS doing your equation. Why don't you GO to a real school you lazy
asshole and find out the truth?