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Some limit proofs

  1. Jun 26, 2004 #1
    How do I show |Rez - Rez0|<E whenever 0<|z-z0|<D is true, where E and D are real number greater than 0, and z is obviously a complex number?

    In other words, proving that the lim of Rez (as z approaches z0)=Rez0.
  2. jcsd
  3. Jun 26, 2004 #2

    matt grime

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    As literally written, your first statement is not true and doesn't imply the second one; it depends on what E and D are.

    However, since |Rez - Rez0| <= |z-z0| is all you need to know you should be able to work it out.
    Last edited: Jun 26, 2004
  4. Jun 27, 2004 #3


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    What you mean is to show that, given any E>0, there exist a D>0 such that |Re(z)- Re(z0)|<E whenever |z-z0|< D. Matt grime's point is that that is very different from saying that |Re(z)- Re(z0)|< E whenever |z-z0|< D for any E and D.

    And, as he said, it follows from the fact that |Re(z)-Re(z0)|< |z- z0|.
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