Talk:Mathematical singularity

The example of the absolute value function having a singularity at x=0 might not be the best, because the absolute value function is not complex differentiable anywhere.

I don't understand the sentence: The algebraic set defined by y2 = x also has a singularity at (0,0), this time because it has a "corner" at that point.

As a set in the plan (i.e., as an imbedded 1-manifold) it is perfectly well behaved. Thought of as a (multi-valued) function it has an infinite slope.

Per haps "... because it has a vertical tangent at that point."

Maybe I'm missing something, which is why I didn't just make the edit myself.... Better not to be bold and confused at the same time. ;-> Jeff 01:40 Apr 10, 2003 (UTC)

Should we add a fourth kind of singularity in complex analysis -- a branch point? Michael Hardy 02:43 Apr 10, 2003 (UTC)

Are singularities in lower dimensions NOT SO IN THE HIGHER DIMENSIONS?This can be proved in this manner-suppose a curve is given ,then write it's parametric equation.treat the parameter as the new dimension .trace the curve in this new coordinate system .sometimes we see the singularity has vanished in the higher dimension.[user:Preetam ]

Shouldn't this page be merged with Singularity theory ? --Piotr Konieczny aka Prokonsul Piotrus 21:37, 12 Jul 2004 (UTC)

Shouldn't this be at singularity (mathematics)? - Fredrik | talk 19:01, 12 Apr 2005 (UTC)

It would be better to have that as disambiguation, I think. Singularity of a function would be one alternate name. There is also singularity of a differential equation to think about. Charles Matthews 19:14, 12 Apr 2005 (UTC)

We seem to bw missing singular matricies (determinant zero). I'd like to add a section about one singularity theory in more details (just 1 paragraph). Also should we include a disambig link to Singularity? --Salix alba (talk) 14:36, 24 January 2006 (UTC)

Connections

A lot of these seem to be closely linked.

Start with a function f : R^m -> Rⁿ. The first derivative dfˈis a linear map or an m by n matrix. f will be singular (in terms of algebraic geometry/singularity theory) when the matrix drops rank. (i.e. is singular).

The commutative algebra ideal's are generilisations of this concept, (think of the ideal generated by the derivatives).

Likewise the singular solutions of ordinary differential equations are simarly linked. --Salix alba (talk) 11:53, 25 January 2006 (UTC)

This may not belong here, but it's the first place that one can add comments to this page - in any case, is "ejaculate" the correct mathematical term for a function that becomes unbounded as it approaches some value (the example on this page being f(x) = 1/x as x > 0)? Is this some sort of vandalism that someone should consider correcting? jmdeur 14:30, 21 March 2008 (UTC)

Number of Types of Singularities in Complex Analysis

There are more than four types of singularities in Complex Analysis. I will correct this mistake if there is no disagreement on this issue. Furthermore, ranking them is appropriate, as the differences are significant. Tparameter 05:53, 9 December 2006 (UTC)

Notation

I (physicist) don't understand what U \ {a} means. Perhaps somebody who does could add a link to something which explains it? Or make it more explicit/obvious? It's in the Complex Analysis section. Thanks --213.49.250.152 (talk) 18:22, 29 July 2009 (UTC)

It means the set U without the element 'a.' (though, 'a' need not be a member of the set U. In which case U\{a} = U.) Got it? I don't think we should change it. It's very common math notation. futurebird (talk) 07:38, 20 September 2010 (UTC)

Etymology: What is the "single" that "singularity" refers to?

Could someone explain what it is that is single that prompts the name "singularity? Gwideman (talk) 00:21, 20 September 2010 (UTC)

if you take the second definition of singular Being the only one of the kind; unique. It most common for a singularity to occur at an isolated point, 1/x has a unique point at 0, which has different behaviour to all other points, hence is singular or a singularity.--Salix (talk): 06:48, 20 September 2010 (UTC)

I have never thought of this before but it makes a lot of sense. I wonder if we can source it? futurebird (talk) 07:39, 20 September 2010 (UTC)

Thanks, Salix, for the reply. I had indeed speculated about that being the origin of the term, but it seems a little indirect -- especially since a function might well have more than a single singularity. So like Futurebird I'm wondering if there's an authoritative source for that account? Gwideman (talk) 21:54, 25 September 2010 (UTC)

Meaning of the word

This

The function g(x) = |x| (see absolute value) also has a singularity at x = 0, since it is not differentiable there. Similarly, the graph defined by y2 = x also has a singularity at (0,0), this time because it has a "corner" (vertical tangent) at that point.

As the section on real analysis says: A point of continuity, which is not a singularity, is a value of c for which f(c − ) = f(c) = f(c + ). Why is the intro using a different defn for the meaning of the word, and where does it get it from?

seems odd to me. I think |x| has no singularities, but its derivative has one at 0. Ditto, y2=x. And calling a vertical tangent a corner is odd, too William M. Connolley (talk) 11:02, 31 December 2010 (UTC)