Question: For a subset S , define the set X as follows: n is in X if and only if the elements 1 , 2 ,

For a subset S, define the set X as follows: n is in X if and only if the elements 1,2,......., n are totally contained in the complement of S. That is, S does not contain any of the element of the set {1,2,3,..., n}.
Show that if 1 does not exist in X, then S has a smallest element.

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