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each of a possibly exhaustive set of classes among which all things might be distributed.

I have doubts about "each of a set". Could we use "each of" with singular noun? If so it seems like there are two possible slightly different meaning for "each of" in general, aren't there?

EDIT: Why we can't say "each of a school" as "each student of a school"?

  • Can you give an example of what you mean? – Keeta Jan 9 at 13:44
  • Please, check the question now. I'v added an additional question. – Oleksiy Plotnyts'kyy Jan 9 at 14:39
  • Change it to each member of a ... set of .... Sets have members and the Axiom of Choice allows one to pick each member. Note that this means taking them one at a time, not all together. Where it overlaps with all is the fact that, if this is true of each member of a set, then it is true for all members of the set. Each, every, and all share the same universal quantifier, but differ in details of presupposition and scope. – John Lawler Jan 9 at 16:20
  • It's great, But I don't get why we can't say "each of a school" as "each student of a school". We also can consider a school as a set of different sorts of things. – Oleksiy Plotnyts'kyy Jan 9 at 16:38
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each of a possibly exhaustive set

This is an abbreviated way of saying:

each member of a possibly exhaustive set

  • Then why we can't say "each of a school" as "each student of a school"? – Oleksiy Plotnyts'kyy Jan 9 at 14:14

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