[FOM] set representation

[Marnes]

Hello,

We know there is two ways to represent/denote sets: by extension and
by comprehension.

I have some philosophical questions about it:

a. A set denoted with the use of ellipsis (...), as in {1,2,4,8,16,
... ,2048}, is by extension or by comprehension?

b. Are there other kinds of representation/denotation?

b1. Is inductively defined set a third kind of
representation/denotation? (Is there a difference between 'define' and
'denote'/'represent' a set?)

b2. Is operations over sets, as A union B, another? (We say "Let x in
A union B, ..."; this A union B is a set. Are we representing/denoting
a set by operation?)

Thank you,
Sincerely,
Marnes