🚀 go-pugleaf

NOTE: NOTHING TO DO WITH THE ORINAL POST
(I think his question was answered long ago!)
Some people have touched on this:
  vector is an element of a special kind of set, a "vector space".  
A set by itself (like R^n) is not a vector space, it also needs some
friends (a field of scalars, a rule for composition, a rule for
multiplication) and some laws by which they all abide (the ten
axioms for a vector space)
At this point we are ready for some neat ideas...

Does a vector have a length? No, note that a norm (or distance function)
was not one of the required friends above!

Does a vector have direction? Hmm After looking at the ten axioms in your
old linear algebra book this should be a little easier to answer.

What about points? Well, points are just elements in a set, so as
such they only have a home, and quite possibly nothing else!


GET REAL!!!

When we start talking about n dimensional euclidean space (R^n)
all of a sudden we introduce lots of structure to things and add
many people to our circle of friends... but it's late and I am tired
of entertaining  (my good friends the vector and point are probably
tired of so many people slandering them too (grin))

Alex

(A mathematician taking computer graphics for fun)

Any mistakes are definitely my own!