In some cases, you might be reading poor-quality mathematical writing.
According to my generalization of some advice from Knuth:[1] in a good math text, definitions of terms are presented as they go along, and they are explicit about what means what. Furthermore, one of the factors that determines the quality of mathematical writing is
- Did you use words, especially for logical connectives, whenever you could have used words (instead of symbols) to express something?
and
> Try to state things twice, in complementary ways, especially when giving a definition. This reinforces the reader’s understanding. [...] All variables must be defined, at least informally, when they are first introduced.
This is repeated:
> Be careful to define symbols before you use them (or at least to define them very near where you use them).
There are some cases where "the general mathematical community is expected to know what you mean," like when publishing papers in some specialized field, but if you're writing a book, these rules hold quite true. Books certainly should explain their notation, especially since the general consensus for certain notations is expected to change over the decades ...
According to my generalization of some advice from Knuth:[1] in a good math text, definitions of terms are presented as they go along, and they are explicit about what means what. Furthermore, one of the factors that determines the quality of mathematical writing is
- Did you use words, especially for logical connectives, whenever you could have used words (instead of symbols) to express something?
and
> Try to state things twice, in complementary ways, especially when giving a definition. This reinforces the reader’s understanding. [...] All variables must be defined, at least informally, when they are first introduced.
This is repeated:
> Be careful to define symbols before you use them (or at least to define them very near where you use them).
There are some cases where "the general mathematical community is expected to know what you mean," like when publishing papers in some specialized field, but if you're writing a book, these rules hold quite true. Books certainly should explain their notation, especially since the general consensus for certain notations is expected to change over the decades ...
[1] http://jmlr.csail.mit.edu/reviewing-papers/knuth_mathematica...