If a complex function has an isolated singularity at a point a and the Laurent series expansion about a involves no negative powers of (z-a), then the singularity is referred to as "removable". Such a singularity is literally removable in the sense that simply assigning an appropriate value to the function at the singularity would make it analytic at that point. For example, the function which is equal to 1 at the origin and zero everywhere else has a removable singularity at the origin. Obviously, assigning zero to this function at the origin makes it analytic there; in general, the correct value to assign is the limit of the function as it approaches the singularity.

A removable singularity can also be defined as a singularity about which the function is bounded.

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