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Math Help - Prove T is bounded

  1. #1
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    Prove T is bounded

    Suppose that S is a nonempty bounded set of real numbers and T is a nonempty subset of S.


    Show that T is bounded
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  2. #2
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    Quote Originally Posted by wopashui View Post
    Suppose that S is a nonempty bounded set of real numbers and T is a nonempty subset of S. Show that T is bounded
    T \subseteq S \Rightarrow \quad x \in T \to x \in S
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  3. #3
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    Quote Originally Posted by Plato View Post
    T \subseteq S \Rightarrow \quad x \in T \to x \in S
    how does this mean T is boundness, bounded above or below?
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    The statement that S is a bounded set of real numbers means that \left( {\exists B > 0} \right)\left[ {\left( {\forall z \in S} \right) \Rightarrow \left| z \right| \leqslant B} \right].
    Therefore T \subseteq S\,\& \,x \in T \Rightarrow \quad \left| x \right| \leqslant B.
    That shows that T is bounded.
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  5. #5
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    Quote Originally Posted by wopashui View Post
    how does this mean T is boundness, bounded above or below?
    Saying that a set of real numbers is "bounded" means it has both upper and lower bounds.
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