# Which one and why: (alphabets and integers sets) OR (alphabets set and integers set)?

Consider the two phrases:

1. alphabets and integers sets
2. alphabets set and integers set

Are both grammatically correct? If so, which one is a better style and why?

My first impression is that both are wrong and that what you want to say is "alphabet and integer sets".

## Why "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:

$\large&space;alphabetSet&space;=&space;\sqsubset&space;German,&space;Cyrillic,&space;English,&space;French&space;\sqsupset$

And the integer set would look like:

$\large&space;integerSet&space;=&space;\sqsubset&space;1,&space;2,&space;3,&space;...,&space;2840238729740027402&space;\sqsupset$

## However...

If you mean to pluralize the alphabets and integers, then you're probably looking at something like this:

• A set of alphabet sets
• A set of integer sets

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".