Real Analysis: Subscripted Index & Countable Order

[IniquiTrance]

I'm encountering subscripts of the form $x_{\alpha_{i}}$, where $i\in \mathbb{N}$, increasingly often in Real Analysis. Is the purpose of the double subscript to show that the index is countable? Another thing that seems to make sense is that the subscript of the index is to define an order on the index where $\alpha_{1}=min({\alpha})$. Any thoughts? Thanks!

 

[quasar987]

I have noticed that, usually, indices taking on "continuous" values will be written with Greek letters (for example indices that take values in R) whereas discrete-valued indices (in Z or N) are written using the usual alphabet.

But this has nothing to do with the number of "piled-up" subscripts!