Defined and undefined: Encyclopedia - Defined and undefined

Defined and undefined

In mathematics, defined and undefined are used to explain whether or not expressions have meaningful, sensible output. These are also known as "well-behaved" and respectively "ill-behaved".

The following algebraic expressions are undefined:

• (see division by zero)
• 0⁰ (however, it is often convenient to define the value of this expression to be 1, e.g. in combinatorics, in the context of power series, and in set theory)
• (however, in probability and measure theory this is usually defined as having value 0)

Undefined values of a function are usually determined by the limit of the function as it approaches the singularity.

See also: mathematical singularity, indeterminate

Adapted from the Wikipedia article "Defined and undefined", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki