Removable Singularity: Is it the Same as a Simple Pole?

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A simple pole, or pole of order 1, is not the same as a removable singularity. A removable singularity can be eliminated by redefining the function at that point, while a simple pole cannot. The integral of 1/z over the unit circle illustrates this distinction. The original poster acknowledged their misunderstanding shortly after posting. The discussion clarifies the difference between these two types of singularities in complex analysis.
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Hi guys,

Is it right to say that a simple pole (pole of order 1) is a removable singularity (and vice versa)?
 
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MMS said:
Hi guys,

Is it right to say that a simple pole (pole of order 1) is a removable singularity (and vice versa)?
No. A pole of order 1 is not removable. Think about the integral of 1/z on the unit circle.
 
I realized it as soon as I posted this thread and forgot to delete it.

Anyway, thank you!
 

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