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Math Help - Well-Ordering Principle

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    Super Member Aryth's Avatar
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    Well-Ordering Principle

    Show that if a and b are positive integers, then there is a smallest positive integer of the form a - bk, \ k \in \mathbb{Z}.
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    Quote Originally Posted by Aryth View Post
    Show that if a and b are positive integers, then there is a smallest positive integer of the form a - bk, \ k \in \mathbb{Z}.
    Consider the set, S = \{a-bk > 0 | k \in \mathbb{Z} \}
    Argue that the set is non-empty and choose the smallest such natural number.
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  3. #3
    Super Member Aryth's Avatar
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    That was too easy, but my professor is a very nervous person and refuses to teach... Instead all of his lectures consist of the words "Uhh" and "Umm".
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