title: How can I proof that a complete binary tree has \lceil n/2 \rceil leaves?
body: <p>Given a complete binary tree with n nodes. I'm trying to proof that a complete binary tree has exactly \lceil n/2 \rceil leaves.
  I think I can do this by induction.</p>
  
  <p>For h(t)=0, the tree is empty. So there are no leaves and the claim holds for an empty tree.</p>
  
  <p>For h(t)=1, the tree has 1 node, that also is a leaf, so the claim holds.
  Here I'm stuck, I don't know what to choose as induction hypothesis and how to do the induction step.</p>