# Thread: Want to know an intuitive but valid way of making metric sets

1. ## Want to know an intuitive but valid way of making metric sets

I just want an intuitive but valid way to describe a set S where every element in S is a coordinate (x, y, z, t) and every component is a real number multiplied by 1 standard unit of measure. This is how I'd like to describe S, but I don't know if it's too inconsistent with convention.

Let Rm = {x m | x is in R, "m" stands for 1 standard meter}. Example, 3.47 m is an element of Rm.

Let Rs = {x s | x is in R+ or x = 0, "s" stands for 1 standard second}. Example, 0.003 s is an element of Rs.

Define S = {(x, y, z, t) | (x, y, z, t) is in Rm3 $\times$ Rs}. Example, (2.2 m, 2.2 m, 2.2 m, 5.0 s) is in S.

So, answers that would probably help me the most would be like either

"There's no serious inconsistency between that and convention; you're not saying anything terribly confused" or
"The proper way to say what you want, and in keeping with the spirit of being similarly intuitive, is . . ." or
"There's a proper way to say what you want but I'm afraid understanding it involves still more background that you obviously don't have."

2. ## Re: Want to know an intuitive but valid way of making metric sets

Originally Posted by Laurien
"The proper way to say what you want, and in keeping with the spirit of being similarly intuitive, is . . ."
The usual way of saying this is to separate coordinates from units of measure. That is, coordinates are elements of simple ℝ4. Besides, we are given three space vectors not lying in the same plane, a time interval with a convention whether future or past is a positive direction, and a point in space-time from where these vectors should start, i.e., the origin. Then, formally, a coordinate system is the bijection between points in space-time and ℝ4 determined by the vectors and the origin.

3. ## Re: Want to know an intuitive but valid way of making metric sets

emakarov, that's exactly what I needed to know. Thank you