Talk:Isolated singularity

Latest comment: 10 years ago by Coffeebrake60 in topic Unintelligible

is it a singularity or isn't it?

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"In complex analysis, a branch of mathematics, an isolated singularity is one that has no other singularities close to it.

Formally, a complex number z is an isolated singularity of a function f if there exists an open disk D centered at z such that f is holomorphic on D − {z}, that is, on the set obtained from D by taking z out."

Either it isn't a singularity, in which case the first sentence is wrong (as it implies that an isolated singularity is a singularity) or it is a singularity, in which case the second sentence is wrong (as it doesn't actually explicity say that it is an singularity, which it should if it is?)

I personally have always seen the description as not needing an isolated singularity to be a singularity (and it being a removable singularity if its Laurent series has no non-zero negative powers in), but this should be rectified one way or the other SetaLyas (talk) 16:47, 18 May 2008 (UTC)Reply

At MathWorld it is defined as a singularity which is isolated:
An isolated singularity is a singularity for which there exists a (small) real number such that there are no other singularities within a neighborhood of radius centered about the singularity.
http://mathworld.wolfram.com/IsolatedSingularity.html
Md2perpe (talk) 11:20, 12 August 2010 (UTC)Reply

Unintelligible

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I can't decipher this at all. Should either be removed or corrected.

"The function here defined as the Maclaurin series   converges inside the unit circle centred in   and has it boundarying circumference as natural boundary" —Preceding unsigned comment added by 184.187.175.87 (talk) 03:30, 6 April 2011 (UTC)Reply

We need to introduce a disambiguation on this concept. There are two concepts of isolated singularity:

  • isolated singularity of a complex analytic hypersurface;
  • isolated singularity of a holomorphic function (of one variable).

Mathematical nomenclature is not perfect. I am rewriting the chapter on Singularity theory. Maybe later I will take care of this. Coffeebrake60 (talk) 08:09, 8 February 2014 (UTC)Reply