Is the naught in $x_0$ an ordinal?

Question

I'm making a spreadsheet containing basic physics terms, symbols, units, defining equations, and a simple English translation of the defining equation. I learned these things in high school, but I'm starting from scratch so that I can make sure I have a better sense of more advanced equations.

For example:

  Var       Name                  Unit   Defining Equation                Logical Meaning               
 ----- --------------- --------- ------ ------------------- ------------------------------------------- 
  _₀    initial ___     ordinal   none   _ₙ, where n = 0     ___ at the start                           
  Δr    displacement    vector    m      Δr = r - r₀         change in spatial position in a direction  
  Δt    time interval   scalar    s      Δt = t - t₀         change in temporal position                

I know my characterizations of displacement as a vector and time interval as a scalar are correct, but is it technically correct to call the n in x_n an ordinal? Or, is there a better descriptor for this?

It's not essential for my spreadsheet, but now I'm really curious.

Answer 1

In this case, I would say it is not an ordinal. When you use, say, $v_0$ to denote the initial velocity, the $0$ subscript is just a decoration used to denote the initial value of a quantity. If we wanted to, we could instead have used some other convention (for example, $v_\ast$).

An alternative setup is to have $v_t$ denote velocity at time $t$. But it would be quite unusual to describe a continuous parameter as an ordinal.

Lastly, when we have a discrete sequence of values $x_0, x_1, x_2, \dots$, we can describe $x_n$ as "the $n$th value". In this case, it makes sense to describe the subscripts as ordinals, though even in this situation the word "index" is generally the one used.