Singularity (mathematics)

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.

  1. ^ "Singularities, Zeros, and Poles". mathfaculty.fullerton.edu. Retrieved 2019-12-12.
  2. ^ "Singularity | complex functions". Encyclopedia Britannica. Retrieved 2019-12-12.
  3. ^ Cite error: The named reference mathworld was invoked but never defined (see the help page).
  4. ^ Berresford, Geoffrey C.; Rockett, Andrew M. (2015). Applied Calculus. Cengage Learning. p. 151. ISBN 978-1-305-46505-3.