title: Why can't a left-recursive, non-deterministic, or ambiguous grammar be LL(1)?
body: <p>I've learned from several sources that an LL(1) grammar is:</p>
  
  <ol>
  <li>unambiguous,</li>
  <li>not left-recursive,</li>
  <li>and, deterministic (left-factorized).</li>
  </ol>
  
  <p>What I can't fully understand is why the above is true for any LL(1) grammar. I know the LL(1) parsing table will have multiple entries at some cells, but what I really want to get is a formal and general (not with an example) proof of the following proposition(s):</p>
  
  <p>A left-recursive (1), non-deterministic (2), or ambiguous (3) grammar is not LL(1).</p>