Math Notes: Notes On Notation
Uppercase and lowercase Roman letters
Uppercase Roman letters are usually used to denote the whole, while lowercase ones are used for parts:
Examples
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Probability Theory
Random variables are usually written in uppercase Roman letters with the particular realisation of that variable designated by the corresponding lowercase character:
So $x_1, x_2, x_3, \ldots x_n$ could be a sample corresponding to the random variable $X$
More: https://en.wikipedia.org/wiki/Notation_in_probability_and_statistics
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Set Theory
When referring to a set as an indivisible entity it is typically denoted using an uppercase Roman letter (for an arbitrary generic set the convention is $S$).
In general however, we are more interested in the components of the set rather than the overarching entity. The elements (even when expressed as an amalgam) are designated by enclosing the notation in brackets: $\big\{\big\}$. So the set of models may be designated using $M$ but the aggregated elements of $M$ are designated using $\big\{M_i\big\}_i$.
For a specific set constructed from our data $D$ however we would designate it $\big\{d_i\big\}$.