singularity: what by definition is it? ( please answer in a single sentence)?
924570
an exception.some thing not consistent with an assumed  theory/relationship-in maths, a point of failure of the equation
616352
I find the concept of an event horizon with a singularity behind it where spacetime curvature becomes infinite fascinating. The idea of spaghettification is intriguing (and a bit frightening!) too. And although scientists reassure us that artificial black holes would be perfectly safe, creating one seems...well, crazy. On the whole, however, I find the whole concept fascinating and wish I had time to take an advanced physics or astronomy class to learn more about it.\n\nI'm afraid I don't understand the other commentator's God reference, though. What black holes have to do with God, or at least the Christian God, is completely beyond me. Last time I checked, the Bible said nothing whatsoever about them.
66821
You can't divide anything by zero, so the answer mathematicians give is that 1/0 is "undefined". \n\nIt is very tempting to think that 1/0 = infinity but there is a consequence...\n\nIf 1/0 = infinity, and 0 times infinity = 1, then what is 2/0? Infinity? \n\nIf we say "yes", then we have to say that 0 times infinity = 1 AND also = 2 (and by implication also 3, 4, 5...). \n\nBut remember that anything times 0 is 0. It only takes the simplest of arithmetic to imagine an empty apple box, and to say "you can ask me for as many as you like - even infinity - but I can only give you zero apples"
711640
Sorry to Sun of Samsa.  I meant to give you a thumbs up!  The Black Hole Singularity is infinitely small (infinite density and ZERO volume).  The effects of the hole can be miles or light years across!
416229
The term "isolated singularity" just refers to a singularity, z_0, in which you can create a neighborhood around it where f is analytic throughout that neighborhood with the exception of the point z_0.  Visualize this as just a single point in the plane.  If this point was a limit point of some series of singularities then it would be very hard to work with, indeed - that's why we want all our singularities to be isolated singularities!\n\nWell, to begin to make sense of your question we first need to know what a Laurent expansion is:  Well, you should be very careful about putting this together, but sloppily said this is an expansion of the form: \nf(z) = Sum(nfrom -infinity to +infinity)a_n(z-z_0)^n\n\nBut what in the world does this have to do with singularities?  Well, if a_n is 0 for all negative n, then we have found a power series expansion for the function - this it is (almost) analytic.  ie, it can be made analytic by "properly" defining f(z_0).  This is the exact notion behind removable singularities - they can be removed!\n\nHow about if all but a finite number of a_n's are zero when n is negative?  Then we could multiply by a large enough value of (z-z_0)^n to make a new function which has a removable singularity.  This is what we call a pole.  It is not removeable, but it can still be worked with, in a way...\n\nFinally if infinitely many a_n with n negative are nonzero then there is no way to make this thing behave like an analytic function near the point z_0.  It is an essential singularity.  A cool result from Picard's theorem says (roughly)that any neighborhood of an essential singularity is mapped to the entire complex plane (except possibly one point).
721127
it's the same as infinity plus infinity infinity times, of course.  ;)\n\nnot to be confused with infinity minus infinity infinity times, which would be the opposite.\n\nalso not to be confused with infinity divided by infinity infinity times, which would be a positive number as close to zero as possible w/o reaching zero.
308805
I predict the value will increase without bound. One factor in  any potential success is the way you integrate around the pole. There could be a strong singularity!
214423
The universe has no end, just as the surface of a sphere has no end. In terms of the surface you can't describe its end, only in terms of a higher dimensional geometry. In that sense, "beyond" is meaningless since it is a term to relate to the same dimension as the universe. It's like "beyond the end of the world" for the surface of Earth -  there is no end, and at some time you might return to where you started from.
174871
its infinite... space in singularity as defined by steven hawking is still expanding and it --> infinite... most dangerous radiations in space r the rays generated by different stars including SUN. clothing that can reflect these kind of rays shd be worn to protect body from these kind of rays
918848
According to general relativity, the matter inside a black hole collapses to a single point: a "singularity".  At this point, the mass density (ρ = m/V) is undefined (because the volume of a single point is zero). \nWe have a lot to learn about extreme cases such as this.
519511
Hard one to understand. but it's something like this:\nIt is said that if you go to the end of the know universe.\nAs you keep going you create space.\nThat nothing before you got there existed.\nSo as the universe expanse it creates it's self, space.
497395
1.\nBecause e to the power minus infinity is 0.
903779
Infinitesimally small.\n\nZero.
244070
Scientist have two theories one is that universe does not have a center point and therefore it cannot have a ending or edge. the other theory is that since the universe is so vast that pin pointing the "edge" of the universe can be harder than it looks.
383637
How do you define what a universe is?  I define the universe as everything there is.  Obviously the set containing everything does not allow the existence of something outside of it.  In other words, if you were to show me evidence of another universe I would say that what you have shown me is part of this universe.\n\nBy my definition there can only be one universe.  Do you have a different definition of what a universe is?
1172315
I don't think we understand either well enough at this point to answer the question. They are both singular in that they both are regions where General Relativity predicts its own breakdown, and as such requires us to come up with new physics to understand them. \n\nThe prediction of these singularities in both cases was shown by the beautiful mathematics discovered by Roger Penrose and Steven Hawking. \n\nNote the following Quote by physicist Lee Smolin.\n\n"It may be conjectured that each black hole of our universe leads to such a creation of a new universe and that, correspondingly, the big bang in our past is the result of the formation of a black hole in another universe." Lee Smolin\n\nOne of the reasons Lee Smolin comes up with this idea is that the constants that our universe is based on seems to be tuned to the production of Black Holes.  That is if you take the fundamental physical constants which we measure and tweak them, you get a reduction in the formation of Black Holes. This he argues is an indication that the birth of baby universes such as our own is directly connected with the existence of Black Holes.\n\nBut to know if there is a direct connection between black holes and baby universes, as Smolin has speculated, is well beyond our current understanding of physics. And the anthropic type arguments that Smolin makes could have other reasons for being true. Our universe is likely fine tuned for our existence for example, and the Black Holes just come along for the ride as it were.
775784
Black holes as mentioned above are a singularity.  Nobody really knows what happens once you cross the event horizon ( the edge of the black hole).  These are very strange events in that they pull everything including light towards them, which contradicts Newtons second law with mass being proportional inversely proportional to mass ( as light has no mass) and Einstein's theory of relativity and the conservation of mass and energy.  All theory we have breaks down when we encounter black holes.\n\nAn interesting theory is that black holes are a link to another universe, matter passing through a black hole and appearing through a white hole in another universe.  This theory has the assumption that there is more than one universe and that they are all linked.  Stephen Hawking's "A Brief history of time" gives many interesting insights.  \n\nHe has recently changed some of his views however with a new theory that a Universe is created by the bumping of one universe into another with black holes becoming the remanents of the reaction, and thus there is no begining or end to time.  He is publishing his ideas soon.  In short however nobody really knows what happens in a black hole.