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:

• <math>\frac{x}{0}<math> (see division by zero)
• <math>\sqrt[0]{x}<math> (since <math>\sqrt[n]{x} = x ^ {1 \over n}<math>)
• <math>0 ^ 0<math>
• <math>\infty – \infty<math>
• <math>0 \cdot \pm\infty<math>
• <math>\frac{\pm\infty}{\pm\infty}<math>

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

See also: mathematical singularity, indeterminate