1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Simple Question regarding C[0,1]

  1. Apr 14, 2005 #1
    So if D={f is an element of C[0,1];f(1) does not equal 1}

    and C[0,1] is the set of complex valued continuous functions on the interval [0,1], is there a function f such that f approaches 1 and f(1) does not equal 1?

    I feel like there has to be one but I am unable to construct one since if the lim as x approaches 1 does not equal f(1)=1, then f wouldn't be continuous right?

    I'm trying to show that D doesn't contain all of its limit points since that would be all that is required to show D is not closed.

    Help with finding this function if there is one please.
     
  2. jcsd
  3. Apr 14, 2005 #2
    I don't understand what you are looking for. If you're trying to show that D is not closed by finding a limit point outside of D, then all you have to do is find a sequence of functions in D that converges to a function not in D.

    For example, take f_n(x) = n / (n + 1). Then every f_n is in D, but the sequence converges to f(x) = 1, which is not in D.
     
  4. Apr 14, 2005 #3
    Yeah, you basically answered my question
     
  5. Apr 14, 2005 #4
    But then why were you asking about trying to find a function such that f(1) != 1 but f(x) -> 1 as x -> 1?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Simple Question regarding C[0,1]
  1. Is 1/x ~ 0? (Replies: 8)

  2. Does 0+0+0+0+0+0+0+ =1? (Replies: 36)

Loading...