Singularity (mathematics)
Point where a function, a curve or another mathematical object does not behave regularly / From Wikipedia, the free encyclopedia
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In mathematics, a singularity is a point at which a given mathematical object is not defined, or a point where the mathematical object ceases to be well-behaved in some particular way, such as by lacking differentiability or analyticity.[1][2][3]
For example, the reciprocal function has a singularity at , where the value of the function is not defined, as involving a division by zero. The absolute value function also has a singularity at , since it is not differentiable there.[4]
The algebraic curve defined by in the coordinate system has a singularity (called a cusp) at . For singularities in algebraic geometry, see singular point of an algebraic variety. For singularities in differential geometry, see singularity theory.