Show that if x=lim a_n for some sequence (a_n) contained in A satisfying a_n not = x,then x is a limit point of A.
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Definition of limit point of a set A: A point x (may or may not be in A) is said to a limit point of A if each epsilon neighbourhood of x intersects with A at otherthan x ...
Solution Summary
A proof involving a limit and sequence is provided.
Real Analysis. A set F subset or equal to R is closed if and only if every Cauchy sequence contained in F has a limit that is also an element of F. ...
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... Taking limit as n goes to infinity, we have. which is. by (3)(4). This is a proof regarding lim sup of sequences. Real Analysis lim sup and lim inf. ...
... This solution explains how to perform the given real analysis questions ... Let y be a positive real number ... Let the limit of this sequence by l . So, we have lim xn ...
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