Well taken, but now we’re approaching the book’s definition which, at the time, I found opaque. Let me see if I can’t massage this into something a bit more colloquial!
Hmm, I think the way you ended up writing it is still a little confusing—you never specified the relation between A and xi, and also I am not sure what it means for a function to “take” an index set."
I gave it another stab (I’m trying to see if I can synthesize your feedback without copying you word-for-word as a comprehension test); please feel free to PM me if it still doesn’t look right. I definitely appreciate the assistance tuning my technical writing, and I think it’s likely this will be helpful to future readers.
Well taken, but now we’re approaching the book’s definition which, at the time, I found opaque. Let me see if I can’t massage this into something a bit more colloquial!
Hmm, I think the way you ended up writing it is still a little confusing—you never specified the relation between A and xi, and also I am not sure what it means for a function to “take” an index set."
Maybe something like: an element of ∏i∈IXi is just a way of assigning to each index i∈I an element of the corresponding space Xi?
I gave it another stab (I’m trying to see if I can synthesize your feedback without copying you word-for-word as a comprehension test); please feel free to PM me if it still doesn’t look right. I definitely appreciate the assistance tuning my technical writing, and I think it’s likely this will be helpful to future readers.
Looks good now.