Give an example of a continuous function on a subset A of and a Cauchy sequence in A in which is not a cauchy sequence in
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Take 0,1] \longrightarrow \mathbb{R}" alt="f0,1] \longrightarrow \mathbb{R}" /> given by and take . Then is certainly not Cauchy.
Crucial point- this sequence converges to a point that is NOT in A. If the converged to a point, a, in A, since f is continuous on A, would have to converge to f(a), and so be Cauchy.
Last edited by HallsofIvy; December 30th 2009 at 08:34 AM.
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About LinkBackson a subset A of
and a Cauchy sequence
in A in which
is not a cauchy sequence in
0,1] \longrightarrow \mathbb{R}" /> given by 