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converse certainly is not. y=1/x has a singular point at {0}, but it's a continuos funtion - hence it can't have any discontinuities. The fact is that discontinuity is a domain-related concept: it has no sense to discuss about continuity in points which not belong to the domain of the given function. On the contrary, singularity is a concept always referring to a broader set than the domain (with the limit case of this broader set = domain): a continuos function may be singular in some extension of its domain (again, y=1/x is continuos in its domain R-{0}, but singular in R}. I think the entry should be fixed, and made coherent with the content of
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835:: IMO, all notions of singularity in mathematics are related to points where some function or its derivative becomes undefined: a curve or a surface defined by an differentiable implicit equation has a singularity if the normal vector is not defined. Nevertheless, it is difficult to give a general definition of "singularity" which covers all the cases. A similar difficulty occurs with the related definition of
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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
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Calling this "original research" is indeed a stretch and a red herring, but it's also not very helpful for this article, and the people reverting it are not "harassing" you. There are plenty of articles either currently discussing or which could plausibly discuss possible definitions of division by
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the second "A Critique of Pure
Physics" looks equally leftfield, and the third is on science fiction. Next we have eight applied science books. The first genuine mathematical books is "Arnol'ds "The Theory of Singularities and Its Applications" with the matching line being "in which the theorems of
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I believe this voice is flawed. It keeps on confusing two concepts which should not be confused, at least here! Singularities and discontinuities are not the same: though it may be true that every discontinuity is alaso singular point (depending of the concept of "well-behavedness" you have), the
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Knowledge is not the place for publishing your original research. Moreover, every addition must be the object of a consensus of the community of
Knowledge editors. As you have been reverted by two different editors, there is no consensus for yours edits, and they are not welcome in Knowledge.
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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?
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mathematical singularity theory provide" so not really a match. On the whole first page of 100 title I can count maybe three mathematical works using the term. Applied scientist can be forgiven for getting the nomeculture wrong but its not a term really used in mathematics.
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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 :
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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
950:: "In general, links should be created for: Relevant connections to the subject of another article that will help readers understand the article more fully; Articles with relevant information; Articles explaining words of technical terms..."
965:“Division by zero singularity” is nowhere defined, and nonsensical, as a pole is not a division by zero. Linking “undefined” is confusing here, as undefined must be understand in its common meaning. Nobody will be help to understand what is
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Yeah, I deleted the y=x example, because it's just a sideways parabola. It doesn't have any undefined areas, or anything else that could be considered singularities. If you count the negative x values, maybe, but that wasn't included in the
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Division by zero is only undefined in certain circumstances. I mean to make the article reflect the true nature of reality, which is that there are many structures where you can divide by zero and get a defined result. 💗
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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.
890:). The current title suggests that "mathematical singularity" is the term commonly used in reliable sources to refer to the topic of this article. That's wrong and misleading. This proposal will correct that. --
1156:. We don't need to have such a discussion literally everywhere that the reciprocal function appears on Knowledge, and in particular it is a distraction in the context of the lead section of this article. –
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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
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However, the restriction of 1/x to real values is useless, and the explanation that was given is too technical, and wrong in the complex case. So, I have fixed this, and this leads to restore the link
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has also the meaning of "unusual". So, I do not know whether "singularity" is derived from the Latin or the French word. In any case, the only relation between "singularity" and "single" is to be
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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
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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.
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The other concern I have is that there are two quite distinct meanings on singularity in mathematics, A) points where a function has a discontinuity and B) and singularities in the context of
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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.--
744:. So "mathematical singularity" is used in technical works as well. Especially in research that are not solely a mathematics paper, but instead is some other field of science. --
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the hits in the first page of Google
Scholar, for "mathematical singularity" are physical articles). Thus "mathematical singularity" is far less common than "singularity" alone.
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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.
769:. When this adjective is used, this appears to be in physics, when classifying the physical singularities, which may or not be explained by mathematical singularities (
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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.
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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
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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. ;-: -->
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Back off. I'd be pleased if I were the one to first claim that division by zero is defined, but I am not. There are many before me, such
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The commutative algebra ideal's are generilisations of this concept, (think of the ideal generated by the derivatives).
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The algebraic set defined by y2 = x also has a singularity at (0,0), this time because it has a "corner" at that point.
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Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.
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Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.
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will be singular (in terms of algebraic geometry/singularity theory) when the matrix drops rank. (i.e. is singular).
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There's other bad examples. Like y=|x|. You can take the absolute value of zero, right? Isn't it just zero?
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A point of continuity, which is not a singularity, is a value of c for which f(c − ) = f(c) = f(c + )
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I have never thought of this before but it makes a lot of sense. I wonder if we can source it?
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prefer using natural disambiguation over parenthetical disambiguation. There are many hits on
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is "curious, strange, peculiar". This explains the use of "singularity". However, the Latin
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Likewise the singular solutions of ordinary differential equations are simarly linked. --
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was linked in the See also section; I've incorporated it into the body of the article (
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Could someone explain what it is that is single that prompts the name "singularity?
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Should we add a fourth kind of singularity in complex analysis -- a branch point?
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by a link to “reciprocal”. So, in the three cases, fgnievinski’s edit is clearly
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The google book results are quite odd. The first three are flaky: one on the
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0)? Is this some sort of vandalism that someone should consider correcting?
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The following discussion is an archived discussion of the proposal.
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The above discussion is preserved as an archive of the proposal.
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exists already as a redirect to this article. I agree with moving
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Per haps "... because it has a vertical tangent at that point."
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Etymology: What is the "single" that "singularity" refers to?
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It would be better to have that as disambiguation, I think.
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http://en.wikipedia.org/Classification_of_discontinuities
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is a technical term, by its own, without the adjective
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928:MOS:LINK
888:contribs
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