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:
  • \frac{x}{0} (see division by zero)
  • \sqrt0{x} (since \sqrtn{x} = x ^ {1 \over n})
  • 0 ^ 0
  • \infty - \infty
  • 0 \cdot \pm\infty
  • \frac{\pm\infty}{\pm\infty}
Undefined values of a function are usually determined by the limit of the function as it approaches the singularity. See also: mathematical singularity, indeterminate

 

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