Cantor's definition of set

Cantor said:

'By a "set" we mean any collection M into a whole of definite,
distinct objects m (which are called the "elements" of M) of our
perception [Anschauung] or of our thought.'
Further, except in a multiset, every element of a set must be unique-
no two members may be identical.

My observation is this:
Surely, these definitions disallow a set whose individual members are
characterized by being sequenced, or heirarchical, or derive their
properties from being in a collection.

For how can we have a set of numbers if, from our definition above, no
two members of a set can be identical?
1) If no two members are identical, then either a number is a
composite (which may allow a heirarchy or sequence) or
2) if number is not a composite then without its members exhibiting a
relationship, a set of numbers is simply a set of numerals.

My question is this: If the above objection against the concept of 'a
set of numbers' (real numbers for example) stands, then how ought we
to correctly define ' a set of numbers'?

.

Relevant Pages

  • Re: Cantors definition of set
    ... these definitions disallow a set whose individual members are ... distinct objects" in any way precludes them from also having such ... composite ... A set may have numerals as members. ...
    (sci.logic)
  • Re: Cantors definition of set
    ... these definitions disallow a set whose individual members are ... distinct objects" in any way precludes them from also having such ... composite ... A set may have numerals as members. ...
    (sci.logic)