Singularity (mathematics)

Point where a mathematical object behaves irregularly

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. For example, the reciprocal function f ( x) = 1 / x {\displaystyle f(x)=1/x} has a singularity at x = 0 {\displaystyle x=0} , where the value of the function is not defined, as involving a division by zero. The absolute value function g ( x) = | x | {\displaystyle g(x)=|x|} also has a singularity at x = 0 {\displaystyle x=0} , since it is not differentiable there.

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