View source for Equivalent conditions to a set being bounded/Statement

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==Statement==
</noinclude>Let {{M|(X,d)}} be a [[metric space]] and let {{M|A\in\mathcal{P}(X)}} be an arbitrary [[subset of]] {{M|X}}. Then the following are all logical equivalent to each other<ref group="Note">Just in case the reader isn't sure what this means, if {{M|A}} and {{M|B}} are logically equivalent then:
* {{M|A\iff B}}. In words "{{M|A}} {{iff}} {{M|B}}"</ref>:
# {{M|1=\exists C<\infty\ \forall a,b\in A[d(a,b)<C]}} - {{M|A}} is [[bounded]] (the definition)
# {{M|1=\forall x\in X\exists C<\infty\forall a\in A[d(a,x)<C]}}{{rFAVIDMH}}
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==Notes==
<references group="Note"/>
==References==
<references/>
{{Theorem Of|Metric Space|Functional Analysis|Analysis|Topology}}
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