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From: nukeymusic on 24 Dec 2009 12:12
Is there a relationship between the following two quantities?

|lim f(z)| and lim |f(z)|

f(z) is a complex function

all help appreciated
nukey
From: José Carlos Santos on 24 Dec 2009 12:15
On 24-12-2009 17:12, nukeymusic wrote:

> Is there a relationship between the following two quantities?
>
> |lim f(z)| and lim |f(z)|
>
> f(z) is a complex function

Yes. If they exist, then they're equal.

Best regards,

Jose Carlos Santos
From: Ki Song on 24 Dec 2009 20:26
On Dec 24, 12:12 pm, nukeymusic <nukeymu...(a)gmail.com> wrote:
> Is there a relationship between the following two quantities?
>
> |lim f(z)| and lim |f(z)|
>
> f(z) is a complex function
>
> all help appreciated
> nukey

If the first quantity exists, then the second one exists and they are
equal
From: G. A. Edgar on 24 Dec 2009 22:04
... and we say the modulus function is *continuous*.

For extra credit, show it is *uniformly continuous*.
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