Consider the two phrases:
- alphabets and integers sets
- alphabets set and integers set
Are both grammatically correct? If so, which one is a better style and why?
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My first impression is that both are wrong and that what you want to say is "alphabet and integer sets".
A set of alphabets, aka "alphabet sets", is a container of alphabets. It's a grouping, or collection, that holds only alphabets and can contain any number of alphabet sets including zero and approaching infinity.
Logically, it would look something like this:
And the integer set would look like:
If you mean to pluralize the alphabets and integers, then you're probably looking at something like this:
The use of "alphabets" is a bit odd. You likely mean "letters" [A, B, C...], unless you literally mean sets of alphabets, as in [Latin, Cyrillic...].
Then you're distinguishing between: letter sets and integer sets [a,b,c] and [1,2,3] OR letter and integer sets [a,1,b,2,c,3]
Speaking as a mathematician, if you mean a set of some, but not all integers, I would say "a subset of the Integers". If however, you mean the set of all the integers, then say "the set of Integers".