Editing Picard theorem (section)

===Little Picard Theorem===
Suppose <math display="inline">f: \mathbb{C}\to\mathbb{C}</math>  is an entire function that omits two values <math display="inline">z_0</math> and <math display="inline">z_1
</math>. Then <math display="inline">\frac{f(z)-z_0}{z_1 - z_0}</math> is also entire and we may assume without loss of generality that <math display="inline">z_0 = 0</math> and <math display="inline">z_1=1</math>.

Because <math display="inline">\mathbb{C}</math> is [[Simply connected space|simply connected]] and the range of <math display="inline">f</math>  omits <math display="inline">0
</math> , ''f'' has a [[Complex_logarithm#Logarithms_of_holomorphic_functions|holomorphic logarithm]]. Let <math display="inline">g</math>  be an entire function such that <math display="inline">f(z)=e^{2\pi ig(z)}</math>. Then the range of <math display="inline">g</math> omits all integers. By a similar argument using the [[quadratic formula]], there is an entire function ''<math display="inline">h</math>'' such that <math display="inline">g(z)=\cos(h(z))</math>. Then the range of <math display="inline">h</math> omits all [[complex number]]s of the form <math display="inline">2\pi n \pm i \cosh^{-1}(m)</math>, where <math display="inline">n
</math> is an integer and <math display="inline">m</math> is a nonnegative integer.

By [[Bloch's_theorem_(complex_variables)#Landau's_theorem|Landau's theorem]], if <math display="inline">h'(w) \ne 0</math>, then for all <math display="inline">{R > 0}</math>, the range of <math display="inline">h</math> contains a disk of radius <math display="inline">|h'(w)| R/72</math>. But from above, any sufficiently large disk contains at least one number that the range of ''h'' omits. Therefore <math display="inline">h'(w)=0</math> for all <math display="inline">w</math>. By the [[fundamental theorem of calculus]], <math display="inline">h</math> is constant, so <math display="inline">f</math> is constant.