Singularity (mathematics) facts for kids

Kids Encyclopedia Facts

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 real function

f(x) = \frac{1}{x}

has a singularity at $x = 0$ , where the numerical value of the function approaches $\pm\infty$ so the function is not defined. The absolute value function $g(x) = |x|$ also has a singularity at $x = 0$ , since it is not differentiable there.

The algebraic curve defined by $\left\{ (x,y):y^3-x^2 = 0 \right\}$ in the $(x, y)$ coordinate system has a singularity (called a cusp) at $(0, 0)$ . For singularities in algebraic geometry, see singular point of an algebraic variety. For singularities in differential geometry, see singularity theory.

Singularity (mathematics) facts for kids

See also