Help me parse the logic of this statement


by Poopsilon
Tags: logic, parse, statement
Poopsilon
Poopsilon is offline
#1
Mar17-12, 11:17 AM
P: 294
So I have this statement that I'm supposed to prove and I cannot for the life of me figure out what parts I'm allowed to assume and what part I am expected to prove, here it is:


The residue of an analytic function f at a singularity a ∈ ℂ is the uniquely determined complex number c, such that the function
[tex]f(z) - \frac{c}{z-a}[/tex]
admits a primitive in a punctured neighborhood of the point a. (end statement)


I know I'm allowed to assume that f is analytic with a singularity at a, but beyond that I just can't tell if it's a biconditional I have to prove, or if it's just a conditional and if so which way. Thanks
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AlephZero
AlephZero is offline
#2
Mar17-12, 11:42 AM
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Thanks
P: 6,388
I think if means prove two things.

1. The residue is a uniquely determined complex number c.
2. f(x) has the property stated.
Poopsilon
Poopsilon is offline
#3
Mar17-12, 02:28 PM
P: 294
Thanks for your input Aleph, but it's not the answer I want to hear lol. Can I get a second opinion?


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