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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- Mar 6th 2010, 11:00 AMwopashuiProve 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 - Mar 6th 2010, 12:12 PMPlato
- Mar 6th 2010, 01:16 PMwopashui
- Mar 6th 2010, 01:47 PMPlato
The statement that $\displaystyle S$ is a bounded set of real numbers means that $\displaystyle \left( {\exists B > 0} \right)\left[ {\left( {\forall z \in S} \right) \Rightarrow \left| z \right| \leqslant B} \right]$.

Therefore $\displaystyle T \subseteq S\,\& \,x \in T \Rightarrow \quad \left| x \right| \leqslant B$.

That shows that $\displaystyle T$ is bounded. - Mar 6th 2010, 02:04 PMHallsofIvy