title: What is the difference between monotonicity and the admissibility of a heuristic?
body: <p>I'm reading over my AI textbook and I'm curious about what the difference is between  monotonicity and admissibility of heuristics (I know they aren't mutually exclusive).</p>
  
  <p>As far as I can tell, an admissible heuristic simply means you are ensured to get the shortest path to a solution if one exists.</p>
  
  <p>What I'm struggling with is the concept of the monotonic property.  Can someone describe this to me in a way I might understand?</p>
  
  <p>Similarly, how can I determine if a given heuristic is monotonic/admissible?  One of the examples given in the book is the 8-Piece Sliding Puzzle.  One heuristic I'm considering is the # of out of place tiles, and intuitively I can say that I know that it is admissible but I have no formal way of showing if it is admissible/monotonic.</p>