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Baby Rudin continuity problem question

  1. Feb 6, 2012 #1
    Sup guys, I was just going over my Baby Rudin and I came across a problem that I don't really know how to get started on.

    Suppose f is a real function defined on R that satisfies, for all x [itex]Limit_{n\ \rightarrow \ 0} (f(x+n)-f(x-n)) = 0[/itex], does this imply f is continuous?

    My first thoughts are that no, it doesn't imply f is continuous, it just implies that f doesn't have any simple discontinuities since [itex]f(x_+) = f_(x_-)[/itex]. I dunno how I can go about showing this though..

    Could anyone nudge me in the right direction?

    Thanks in advance!
     
  2. jcsd
  3. Feb 6, 2012 #2

    tiny-tim

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    hi genericusrnme! :smile:
    does it ? :wink:
     
  4. Feb 6, 2012 #3

    HallsofIvy

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    Well, what, exactly, do you mean by a "simple" discontinuity? If f(x)= 1 for all x except 0 and f(0)= 0, that looks like a pretty simple discontinuity to me!
     
  5. Feb 7, 2012 #4
    Ah yes, you're completely right
    f(x+) = f(x-) but f(x+) isn't necessarily equal to f(x)

    Yep, I just got that

    Thanks guys!
     
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