Help me parse the logic of this statement

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In summary, the conversation is about proving a statement involving the residue of an analytic function at a singularity and the difficulty in determining what assumptions are allowed and what needs to be proven. The speaker believes they need to prove two things - that the residue is a uniquely determined complex number and that the function has a specific property. They are seeking a second opinion.
  • #1
Poopsilon
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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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  • #2
I think if means prove two things.

1. The residue is a uniquely determined complex number c.
2. f(x) has the property stated.
 
  • #3
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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