<h2>Numbers</h2>

<p><strong>Trick Question</strong>  Is this a number:  256? </p>

<p>No, it is a <em>representtion</em> of a nuber.  Here are two 
more representations of the same number using Roman numerals and 
tally marks.</p>

<pre> 
CCLVI

IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
</pre>

<p><strong>Question</strong> Suppose I have two collections of objects A and B.
How can I tell which is bigger WITHOUT COUNTING?</p>

<p>Pair the objecdts off until one set is exhausted.<p>

<ul>
    <li>If there no leftovers, A and B have same size.</li>
    <li>If A has leftovers, A is bigger.</li>
    <li>If B has leftovers, B is bigger.</li>
</ul>

<p>Number is this noation of "samesizeness."  </p>

<p>Here is the enrollement at NCSSM.</p>

<pre>
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
</pre>

<p>Tally marks have some advantages. Addition is easy; just concatenate.
</p>

<p>Here is how to subtract.  Erase the last tally mark in each operand.
do so until the second operand is gone.

<pre>
IIIIIIII - IIII 
IIIIIII - III 
IIIIII - II 
IIIII - I 
IIII       &larr; Et Voila!
</pre>

<p>Look ma!  No Wormwoodean borrowing!!!</p>

<p>There are no signed numbers.</p>