title: Professor claims two distinct maximum flows implies an "infinite number of maximum flows"
body: <p>I will say right out that this is a homework problem that I have attempted for hours and I am not getting anywhere.  The problem states "Suppose there exist two distinct maximum flows <em>f₁</em> and <em>f₂</em>. Show that there exist infinitely many maximum flows."  Now, I needed some clarification on what he meant by distinct and the email reply I received stated, "<em>f₁</em> and <em>f₂</em> are distinct if there exists <em>(u,v)</em> such that <em>f₁(u,v) ≠ f₂(u,v)</em>."  So going off of this definition of distinct, I find the problem statement to not be true.  </p>
  
  <p>Take for example this graph: </p>
  
  <p><img src="https://i.stack.imgur.com/5VYrk.jpg" alt="example graph"></p>
  
  <p>It has two distinct maximum flows but no more.  What do you guys think?  Maybe I am going about this is the wrong way.</p>