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→Distinction from set-valued relations: rm section based on a single book that contradicts common terminology. In any case, if this books is sufficiently notable to be cited, this must not be done in such a prominent way |
→Concrete examples: Using sqrt(x) on real numbers to denote a multivalued function contradicts common terminology, I think it's reasonable to point this out |
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==Concrete examples==
*Every [[real number]] greater than zero has two real [[square root]]s, so that square root may be considered a multivalued function. For example, we may write <math>\sqrt{4}=\pm 2=\{2,-2\}</math>; although zero has only one square root, <math>\sqrt{0} =\{0\}</math>. Note that <math>\sqrt{x}</math> usually denotes only the principal square root of <math>x</math>.
*Each nonzero [[complex number]] has two square roots, three [[cube root]]s, and in general ''n'' [[nth root|''n''th roots]]. The only ''n''th root of 0 is 0.
*The [[complex logarithm]] function is multiple-valued. The values assumed by <math>\log(a+bi)</math> for real numbers <math>a</math> and <math>b</math> are <math>\log{\sqrt{a^2 + b^2}} + i\arg (a+bi) + 2 \pi n i</math> for all [[integer]]s <math>n</math>.
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