## Quick Reference

A point on a curve where there is not a unique tangent which is itself differentiable. It may be an isolated point, or a point where the curve cuts itself such as a cusp.

A point at which a complex function is not analytic. For example, has a singularity at *z*=0, and is said to be an isolated singularity because there is no other singular point in the neighbourhood of *z*=0 (in fact it is the only singular point of that function). If there is a value which *f*(*z*) could be assigned at the singular point which would make the function analytic at that point, then it is termed a removable singularity. In the above example |*f*(*z*)| → ∞ as |*z*| → 0 so this is not a removable singularity, but for which also has a singularity at *z*=0, if we define *f*(0)=1 the function is analytic at 0, and this is an example of a removable singularity.

*Subjects:*
Mathematics.

## Related content in Oxford Index

##### Reference entries

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.