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Math Help - simple complex limti proof

  1. #1
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    simple complex limti proof

    I'm having difficulty showing that:

    \lim_{z \leftarrow z_o} \text{Re}\ (z) = \text{Re}\ (z_0)

    it just seems like an obvious
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  2. #2
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    Quote Originally Posted by lllll View Post
    I'm having difficulty showing that:

    \lim_{z \leftarrow z_o} \text{Re}\ (z) = \text{Re}\ (z_0)

    it just seems like an obvious
    You have to show that for all \varepsilon > 0 there exists a \delta>0, such that whenever:

    |z-z_0|<\delta

    then

    | {\rm{Re}}(z) - {\rm{Re}}(z_0)|<\varepsilon

    (In this case \delta=\varepsilon will do which is perhaps why this seems obvious)

    RonL
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