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Identifying the name of a theorem

  1. Jan 12, 2015 #1
    I can't find sufficient material for this theorem in my own languages so I have to resort to English, however, googling "Heine criterion" yields nothing significant so I think, once again I just can't get its English name right.

    Limit of a function: Heine criterion:
    Given [itex]f\colon D\to\mathbb{R}, \lim\limits_{x\to a} f = A\Leftrightarrow \forall (x_n)\to a\colon x_n\neq a \Rightarrow f(x_n)\to A[/itex]
    In words: A is a limit of f as x approaches a if and only if for every sequence [itex](x_n)[/itex] converging to a such that [itex]x_n\neq a[/itex] their respective function f values converge to A.

    EDIT: tiny error correction
    Last edited: Jan 12, 2015
  2. jcsd
  3. Jan 12, 2015 #2

    Stephen Tashi

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  4. Jan 12, 2015 #3
    In our lectures it's specifically referred to as the Heine criterion, I just find it odd that googling this yields no result. A bit similar when I tried to look up a lemma given in our lectures as "Kuratowski-Zorn lemma", in most sources I just found it as "Zorn's lemma" which is curious.. 1st and 2nd world conflicts from the "good" ol' days?

    Assuming you mean 5.1.15 in the notes, then yes, it does look the same. Thanks, I now know what to look for.
    Last edited: Jan 12, 2015
  5. Jan 13, 2015 #4
    Sequential criterion for limits.
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