coordinates are fixed

Mathematical - Physical

What is the distance from (0,0,0) to (2,0,0) ?

The physicists...we require measurement, to physically go from one to the other, and calibrate the rate of speed and the duration time using instruments to approxiamate a value, which can only be accurate as the physical devices used to measure with....indeed, never exact!
The mathematicians... A Cartesian system is imagined...it has no thickness...it can NEVER physically exist. When we are given such a system, we can calculate that distance mathematically as EXACTLY 2. It is inhererent to what a Cartesian coordinate system is.

intellectual, imagined, abstract, created
"impossible to manifest perfectly: physically"
examples....point, line, square, circle, cube, Cartesian coordinate system

Used to represent some actual physical reality, whereby, every number is not just a number, but also represents some, as yet to be defined, value or quantity. The number 2 is always mathematically exactly twice the "unexpressed" value or quantity of the number 1, no matter what initial evaluation is given to the number 1. For example, what is two times 1, mathematically the answer is 2. - no problem.

Physics - only one object/event per location
Math - one imagined point per imagined system per location the same location could have dozems of uniquely named points


Now, what if you multiple one apple by 2? Mathematically the answer is 2 apples. However, could 2 crisp, ripe, succulent, right off the tree, picked at the right time of the season, worm-less, Cortland apples that I now hold in my hand, ever be equal to, 2 nearly identical to one another, post-season, wormy, partially squashed, insecticide sprayed, sour crab apples, that you must wait until tomorrow to possibly receive…for example?

Physically there is a problem with apple equality. This mathematical technique works great for just numbers… their inter-relationship is based upon the continuity of evaluation… all intervals between 0, 1, 2, 3, etc. being exactly equivalent.
When numbers are applied to any physical reality, this continuity needs to be in place in order that the numbers reflect an underlying reality.

real, tangible, manifested, exists

examples....neutrino, photons, quarks, mesons, leptons, sub-atomic particles, protons, atoms, anti-matter

Present in only one of two forms:

1 that which inherently possesses substance/mass...indestructible unit/equal spheres

2 "empty space" ....that which does not inherently possess substance; those physical locations of the mathematical point designations.