eran_rathan wrote:steve waterman wrote:???

I can't really follow what you are saying here, but I'm going to try (again) to explain what I think you are trying to say.

Coordinate system, and points P and Q which are non-coincident. P represents the origin of the coordinate system, Q is a point at (x,y,z).

1. Create a new coordinate system at (x,0,0) and call it

Blue, where x is the X-value of Q (making Q the origin point of

Blue). P

_{Blue} is now at (-x,y,z).

2. The distance between Q and P, regardless of coordinate system used, is

constant.

3. Distances between coordinates can

only be measured using the same system, otherwise you are comparing apples and oranges.

Coordinate system, and points P and Q which are non-coincident. P represents the origin of the coordinate system, Q is a point at (x,y,z).

NO. ...selected point P in Red is not an origin...as it is at (2,0,0) in the Red system.

No . selected point Q at (2,0,0) in Blue is not at the VARIABLE (x,y,z)...it is SELECTED/named/given a CONSTANT VALUE for (x,y,z) = (2,0,0) in the Blue system.

Does that makes any clarity for you?

btw, you could not possibly follow ANY consequential math logic here...as you were using the wrong parameter from the get go.

WOW...by virtue of trying to do "bottom of the page writing" it is so hard to follow who is saying what...way confusing. So, it is now is a presentation form that can stand-alone...even any depictions are not necessary as it is hopefully, all trimmed to some basics, itemized directly below.......................................................................................................................................................................

MY mathematically GIVEN....

1 Red and Blue coincident system ( where coincidence implies equality in all mathematical aspects )

2 selected point P in Red at (2,0,0)

3 selected point Q in Blue at (2,0,0)

the transformations between systems results with...

using the GalileanRed left 3

then Q in Blue at (2,0,0) trans to P in Red at (5,0,0)

OR

Blue right 3

then P in Red at (2,0,0) trans to Q in Blue at (-1,0,0)

my mandateRed left 3. then

Q in Blue = (2,0,0) transforms to Q in Red = (5,0,0) AND P in Red = (2,0,0) transforms to P in Blue = (-1,0,0)

Blue right 3. then

Q in Blue = (2,0,0) transforms to Q in Red = (5,0,0) AND P in Red = (2,0,0) transforms to P in Blue = (-1,0,0)

observation 1...

comparing the transformation results of Red left 3 against that of Blue right 3...

the Gailean has opposing/variant/variable/inconsistent/conflicting results.

my mandate has equivalent/equal/identical/proper/mathematical valid results.

observation 2...

since coordination is affixed to its' own system, then If one of two coincident system relocate from that coincidence,

then

Red (x,y,z)= Blue (x',y',z') is true.

observation 3

the Galilean contends that

Red (x,y,z)= Blue (x',y',z') - d, is true

Conclusion: both equations cannot be mathematically correct

...................................................................................................................................................................

steve waterman

"While statistics and measurements can be misleading, mathematics itself, is not subjective."

"Be careful of what you believe, you are likely to make it the truth."

steve