Help in building a formal proof

  1. A is a non empty group which is bounded from the top.
    prove that S=sup A if and only if S is the upper bound of of A
    and there i a series of numbers An (An which belongs to A) so An->S

    i was proposed a general solution:
    presume that supA=S
    show that there is a series An (An belongs to A) so lim An=s (n goes to infinity)

    and there is a sketch here:

    how to make a formal proof for it??
  2. jcsd
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