algebra question

an eminent music theorist wrote me in an e-mail:

"Paul, this is really basic algebra, and this time I suggest that you
consult
a mathematician or a textbook. In any event, once you have created
equivalence classes, you can only refer to a given class *as a
whole*--not
to its individual members."

can gene confirm or deny?

--- In tuning-math@yahoogroups.com, "wallyesterpaulrus <wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:
> an eminent music theorist wrote me in an e-mail:

>
> "Paul, this is really basic algebra, and this time I suggest that you
> consult
> a mathematician or a textbook. In any event, once you have created
> equivalence classes, you can only refer to a given class *as a
> whole*--not
> to its individual members."
>
> can gene confirm or deny?

I'm a little reluctent to enter a conversation without knowing what it's about, but I won't let that stop me.

If S is an equivalence class, we refer to the class itself as S, and would refer to an element x being a member of the class S in one of two ways:

(1) x \in S (where "\in" is TeX for the "element of" symbol) or

(2) x S s, where s is known to be an element of S, or is used to represent S.

I think it's neat a distingished theorist is writing to you; I was impressed when a distinguished composer emailed me yesterday, but a theorist is someone we could try to drag onto Yahoo and find out what the conversation is about.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith <genewardsmith@j...>" <genewardsmith@j...> wrote:
> --- In tuning-math@yahoogroups.com, "wallyesterpaulrus <wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:
> > an eminent music theorist wrote me in an e-mail:

> If S is an equivalence class, we refer to the class itself as S, and would refer to an element x being a member of the class S in one of two ways:
>
> (1) x \in S (where "\in" is TeX for the "element of" symbol) or
>
> (2) x S s, where s is known to be an element of S, or is used to represent S.

This should be

(2) x R s, where R is an equivalence relation for which S is an equivalence class, and s represents S. That is

S = {x | x R s}