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=== Natural logarithm === Consider the [[natural logarithm]] function mapping the [[real number]]s to themselves. The logarithm of a non-positive real is not a real number, so the natural logarithm function doesn't associate any real number in the codomain with any non-positive real number in the domain. Therefore, the natural logarithm function is not a function when viewed as a function from the reals to themselves, but it is a partial function. If the domain is restricted to only include the [[positive reals]] (that is, if the natural logarithm function is viewed as a function from the positive reals to the reals), then the natural logarithm is a function.
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