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If a set A is both open and closed then it is R(set of real numbers)by seema283k
Tags: theorem 
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#1
Sep1009, 10:20 AM

P: 4

if a set A is both open and closed then it is R(set of real numbers) how we may show it in a proper way



#2
Sep1009, 02:36 PM

P: 810

My approach for this proof would be to consider this. An open set contains none of its boundary points. A closed set contains all its boundary points. The only way for this to be possible is for A to have NO boundary points at all. Show how {} and R are the only two sets that have this property. 


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