The weblog of Nicholas Chapman CompressionPosted 27 Oct 2013 For any given finite string, there is a compression method (an invertible (one-to-one) function) for which the finite string is compressed to the empty string. Proof: Given a finite string i, we can construct the one-to-one function $$C_i$$: $$C_i(x) = \begin{cases} \epsilon &\mbox{if } x = i \\ i &\mbox{if } x = \epsilon \\ x &\mbox{otherwise} \end{cases}$$ which means that $$C_i(i) = \epsilon$$ i.e. the input string $$i$$ is mapped to the empty string $$\epsilon$$, and $$C_i(\epsilon) = i$$ i.e. the empty string $$\epsilon$$ is mapped to $$i$$, and for all other strings $$C_i(x) = x$$ i.e. we have the identity mapping.Do you have a comment or feedback about this blog post? Please email me.< Back All content by Nicholas Chapman. Static Pages on this website Our software Indigo Renderer Chaotica