Talk:Isolated singularity

is it a singularity or isn't it?

"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)

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)

Unintelligible

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

"The function here defined as the Maclaurin series $\sum _{n=0}^{\infty }z^{2^{n}}$ converges inside the unit circle centred in $0$ and has it boundarying circumference as natural boundary" —Preceding unsigned comment added by 184.187.175.87 (talk) 03:30, 6 April 2011 (UTC)

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)