Real Analysis: Subscripted Index & Countable Order

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The discussion centers on the use of double subscripts in Real Analysis, specifically the notation x_{\alpha_{i}} where i belongs to the natural numbers. The double subscript serves to indicate that the index is countable and helps define an order on the index, with the minimum value represented by \alpha_{1}. Additionally, it is noted that continuous indices are typically denoted by Greek letters, while discrete indices utilize standard alphabetic characters.

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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!
 
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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!
 

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