title: proving that huffman's algorithm can produce a codeword of length 1 when frequency greater than 0.40
body: <p>If I have a set of symbols and frequencies: 
  A - 0.1
  B - 0.40
  C - 0.2
  D - 0.23
  E - 0.15
  F - 0.17 </p>
  
  <p>The Huffman algorithm will produce codewords that are only <strong>greater</strong> than length 1. </p>
  
  <p>But when I change a frequency to be greater than 0.40, it will produce a codeword <strong>of</strong> length 1 and greater. How can construct a proof that proves that this is the case for any set of symbols, not just this one? </p>