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Limit of sequence of functions

  1. Jul 31, 2011 #1
    Hi. When we say that [itex]\displaystyle \lim_{n \to \infty}f_n(x)=g(x)[/itex], do we mean that [itex]f_n[/itex] is pointwise or uniformly convergent to [itex]g[/itex]?
  2. jcsd
  3. Aug 1, 2011 #2
    The convention is that pointwise is assumed unless you specifically say it's uniform.
  4. Aug 1, 2011 #3

    I like Serena

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    The x is unspecified, meaning your statement is incomplete.
    Usually it is implied that you mean "for each x in the applicable domain of the functions".
    This also means that you imply "pointwise convergent".

    If you left out x completely by saying [itex]\displaystyle \lim_{n \to \infty}f_n=g[/itex], you would specify "uniform convergent".
  5. Aug 1, 2011 #4
    Thanks, both of you.
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