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Math Help - Uniform convergence

  1. #1
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    Uniform convergence

    Is a horizontal line uniformly convergent??

    Thanks.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Benmath View Post
    Is a horizontal line uniformly convergent??

    Thanks.
    as in f_n(x) = c for all n and x converging uniformly to f(x) = c (where c is a constant)?

    you tell me, does this satisfy the definition of what it means to be uniformly convergent?
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  3. #3
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    I would say yes it is uniformly convergent. I have a line x=2.

    So f_n(x)=2 and f(x)=2. Their difference is 0 implying uniform convergence.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Benmath View Post
    I would say yes it is uniformly convergent. I have a line x=2.

    So f_n(x)=2 and f(x)=2. Their difference is 0 implying uniform convergence.
    x = 2 is a vertical line. so unless you are interpreting it like f_n (y) = 2 or something, it won't make sense. but yeah, a difference of zero everywhere implies uniform convergence
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  5. #5
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    Oops that was dumb, I meant the line y=2. Sorry. Thank you!
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