title: The Integrality theorem in maximum flow
body: <p>The integraloty theorem tells us that if all capacities in a flow network are integers, then there is <strong>a</strong> maximum flow where every value is an integer</p>
  
  <p>But the most remarkable part is the existence, not every maximum flow!
  Which means this statement doesn't claim <strong><em>every</em></strong> maximum flow is integer-valued</p>
  
  <p>I cannot figure out why if all capacities are integer, but there exists a maximum flow is not integer-valued!!</p>
  
  <p>Or did I just get wrong idea of this theorem that tries to tell me?</p>