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In article <4g63cj$p42@news.sdsmt.edu>
           kbs3387@silver.sdsmt.edu "Kevin Stone" writes:

> : A point only exists in _one_ dimension. Hence no magnitude, nor
> : direction, ie. a point is not a vector.
> 
>     A point can exist in ANY dimension.  A vector can exist in any 
>     dimension.  The only difference is that a point has no "substance", 
>     and a vector does.

More or less, yes.  A point is just a point.  It has a position (you can also
give it other fun things like mass and velocity, but thats another thing
entirely).  Note that you cannot specify any numbers for this position,
because "everything is relative".  All you can do to locate this point is
to specify its displacement from another point (a reference).

This displacement is it's position vector, and all it is doing is referring
that point to another.  There are no absolute co-ordiantes which a point can
have.  It's position vector from another point is just another of the point's
'properties', like mass or velocity.  Remember that points are completely
abstract entities.

Saying a point can only exist in one dimension is completely and utterly
wrong.  A point itself could be said to have 0 dimensions (lines are 1-d).
But that is a misnomer, as what it really means is that it has zero length in
every dimension.  That does not mean it cannot exist in higher dimensions --
everyone accepts lines existing in 2d space, it is simply considered as a
plane of width 0.

So basically, points do not have a location (numerically).  They do have
a set displacement from another point.  This is completely useless unless
you have more than one point, upon which you can do fun things like measure
the distance between those points.

To relate this back to computer science =) you deal with points as an 'object'
yet you can *only* access that object via its position vectors.  So, in
effect (which is what counts):  point == position vector.  Note that this
takes care of the 'you can't add 2 points' argument because you cannot add
two *position* vectors.

Practically, everything of n dimensions can exist in space of >n dimensions --
you just zero the extra parameters.
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