In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability.
From Wikipedia
A more technical definition is available at Wolfram's Mathworld:
In general, a singularity is a point at which an equation, surface, etc., blows up or becomes degenerate. Singularities are often also called singular points.
Singularities are extremely important in complex analysis, where they characterize the possible behaviors of analytic functions. Complex singularities are points z_0 in the domain of a function f where f fails to be analytic. Isolated singularities may be classified as poles, essential singularities, logarithmic singularities, or removable singularities. Nonisolated singularities may arise as natural boundaries or branch cuts.
so we need to be more precise here ... So discuss .... don't be so farklempt as the SSL crew would say.
Singularity
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