TITLE: A Question on Singularity
QUESTION [1 upvotes]: I am not aware of GR, but due to curiosity i have a question in my mind. Please let me know if it is inappropriate to ask here.
My question is about singularity. I am under the assumption that singularity means in mathematical terms equivalent to a discontinuity in a function. My question is what type of discontinuity are the ones corresponding to Penrose-Hawking singularity theorems and also to the the naked singularity ?
by type i mean

removable (left and right limits exist and are equal 
         but not equal to the function value at that point).
a jump type discontinuity (left and right limits exists and are 
       not equal to each other).
Oscillating discontinuity (as described as described in the above given link)

REPLY [2 votes]: The formal definition is 'a point through which a geodesic cannot be extended'.  It can be a point where the curvature is infinite, as said above, but the concept is a little more general--it is a point at which there is no smooth way to extend a path into the future.  Formally, what the singularity theorems show is that, when the curvature obeys certain conditions, and you have positive energy, then certain geodesics must end in a finite proper time.  
Note the contrast with Minkowski space, where a particle moving in a straight line is free to continue moving in a straight line forever, always tracing out more and more proper time.

REPLY [0 votes]: I suspect mathematically singularity means $\frac{1}{0}\rightarrow\infty$. The size goes to zero and the math blows up. In fact, the size does not have to be zero for singularity to exist. If you think of trying to force a wave to exist in a sub-harmonic wavelength (size), it also makes the math blow up.
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