title: How many double numbers are there between 0.0 and 1.0?
body: <p>This is something that's been on my mind for years, but I never took the time to ask before.</p>
  
  <p>Many (pseudo) random number generators generate a random number between 0.0 and 1.0. Mathematically there are infinite numbers in this range, but <code>double</code> is a floating point number, and therefore has a finite precision.</p>
  
  <p>So the questions are:</p>
  
  <ol>
  <li>Just how many <code>double</code> numbers are there between 0.0 and 1.0?</li>
  <li>Are there just as many numbers between 1 and 2? Between 100 and 101? Between 10^100 and 10^100+1?</li>
  </ol>
  
  <p>Note: if it makes a difference, I'm interested in Java's definition of <code>double</code> in particular.</p>