🚀 go-pugleaf

Assume that a coordinate system of xyz-axes has been chosen. Then both a
point P and its position vector \uparrow(OP) are represented by the same
triple (a,b,c). Hence we are allowed to write P=(a,b,c)=\uparrow(OP), i.e.
P=\uparrow(OP). With this simple notation, we have the simple formula:
\uparrow(AB)=B-A.

Question: DO you accept or reject the notation P=\uparrow(OP)?

The advantage of identifying a point and its position vector can be seen
from some formulas such as 

(a) point-normal form of the plane through A with normal N, (P-A).N=0

(b) mid-point of A,B is  (A+B)/2

(c) \uparrow(AB)x\uparrow(AC)=(B-A)x(C-A)

(d) point-direction form of a line,  P=A+t D, t is real.

Otherwise we have to write 

(\uparrow(OP)-\uparrow(OA) ).N=0

(\uparrow(OA)+\uparrow(OB))/2

\uparrow(AB)x\uparrow(AC)
=(\uparrow(OC)-\uparrow(OA))x(\uparrow(OC)-\uparrow(OA))

\uparrow(OP)=\uparrow(OA)+t D, but you still fail to express the point P.

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We all know that a point in the plane is an ordered pair (x,y) and a point
in the space that is on xy-plane is an ordered triple (x,y,0). Everybody
knows that (x,y)<>(x,y,0) and yet we all accept that the xy-plane is a
subset of xyz-space and therefore we are allowed to identify (x,y)=(x,y,0)
as long as there is no misunderstanding.

===================================================

We all know that the real numbers and complex plane are constructed in
completely different way, but we are happy to accept that real field is a
subset of the complex field.

We accept that the completion K of a uniform space X or a metric space is
completely different from X itself but we are happy to accept X as a dense
subset of K.

There are so many examples that whenever two objects are isomorphic, we do
not want to distinguish them. Why should we be so cynical to reject the
identification of a point and its position vector whenever a coordinate
system HAS been chosen which is the case for high-schools and first-year
universities.

Same question again: DO you accept or reject the notation P=\uparrow(OP)?

Next question: Should we or should we not persuade the textbook writers to
adopt the notation P=\uparrow(OP)?

Final Question: Does it reflect the psychological insecurity of the older
teaching staff in power and in position to accept something is logically
correct, conceptually correct and mathematically correct but has an
unpopular notation. The bureaucrats want to simplify their forms. Why do
the technocrats want to insist on complication?? Is there any
standardization organization that I can take this case to them?

I DO need your public opinion URGENTLY. Please cast you vote, one way or
another. Thank you in advance. Thank you for supporting the global
democracy of mathematical education.

Your opinion will be copied to a certain web-site and will be available to
the global public community. If you want to insist on your own copyright
and do not want your opinion to be recorded, please indicate in your
posting.


Dr. MA, Math Dept, UWA

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