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:

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

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

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