Question

Define space? and how we will express it mathematically?

Answer 1

There are a myriad of intepretations to the problems of defining "space". The most simplistic way is to look at space as a 3 dimensional vector space over the real numbers, ie \[\Bbb R^3\] Since this is a vector space, we can attribute a coordinate system to it. Though we can pick a number of different systems, the most basic is the one you are most familiar with, namely describing points using the coordinate (x,y,z), relating to the points distance along lines parallel to the x-, y-, and z-axes (respectively).