title: Gaps between successive floating point numbers
body: <p>(all numbers discussed are in decimal)</p>
  
  <p>lets say we have a floating point data type that is like :</p>
  
  <blockquote>
    <p>m * 10 ^ e</p>
  </blockquote>
  
  <pre><code>where m is the mantissa . and max mantissa size is 1 ( 0 &lt;= m &lt;= 9);
  
  e is the exponent and its size is  -1 &lt;= e &lt;= 1
  </code></pre>
  
  <p>we say our data type Max value is 90 and its Min value is 0</p>
  
  <p>BUT : that does not mean we can represent all numbers that are in this limit .
  we can only represent 27 numbers ( 9 * 3 ) excluding zero.</p>
  
  <p>specifically we can't represent 89 in this way since it has a two digit mantissa 
  (and non of them are zero).</p>
  
  <p>so technically analogous to the above descriptions . in a float data type (in any programming language) there must be some integers between Max and Min values that we cannot store in a float data type . </p>
  
  <p>is the above argument sound . if it is please give an example how to show this in java or c ?  </p>