Editing Cardinal number (section)

==== Logarithms ====
Assuming the axiom of choice and, given an infinite cardinal ''κ'' and a finite cardinal ''μ'' greater than 1, there may or may not be a cardinal ''λ'' satisfying <math>\mu^\lambda = \kappa</math>. However, if such a cardinal exists, it is infinite and less than ''κ'', and any finite cardinality ''ν'' greater than 1 will also satisfy <math>\nu^\lambda = \kappa</math>.

The logarithm of an infinite cardinal number ''κ'' is defined as the least cardinal number ''μ'' such that ''κ'' ≤ 2<sup>''μ''</sup>. Logarithms of infinite cardinals are useful in some fields of mathematics, for example in the study of [[cardinal invariant]]s of [[topological space]]s, though they lack some of the properties that logarithms of positive real numbers possess.<ref>Robert A. McCoy and Ibula Ntantu, Topological Properties of Spaces of Continuous Functions, Lecture Notes in Mathematics 1315, [[Springer-Verlag]].</ref><ref>[[Eduard Čech]], Topological Spaces, revised by Zdenek Frolík and Miroslav Katetov, John Wiley & Sons, 1966.</ref><ref>D. A. Vladimirov, Boolean Algebras in Analysis, Mathematics and Its Applications, Kluwer Academic Publishers.</ref>