Re: Request for help in proper notation of ordinals.

On Tue, 28 Aug 2007, Scott wrote:

Hi: Given any set S with transfinite cardinality x, what is the
correct notation for showing a list of this set. For example (using
latex notation):

S = { s_0, s_1, s_2, ..., s_{w_x} }

Would this be the correct notation? Or would it just be

S = { s_0, s_1, s_2, ... }

Restricting xi to ordinals and kappa to cardinals, ie initial ordinals, a
set S of cardinality kappa can be represented as a well ordered set with
S = { a_xi | xi < kappa }

The representation is not unique, just the most efficient or slickest.
It is not possible to 'list' the reals for a list is a set of the form
{ a_n | n in N }

.