Defined and undefined
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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