 <p>Basically, in mathematics, there is a concept of "<a href="http://en.wikipedia.org/wiki/Lebesgue_measure" rel="nofollow">Lebesgue Measure</a>". This assigns values to length, area, volume, etc. by manipulating the interval <code>[0,1]</code>.</p> <p>Here's an intituitive explanation. A point at <code>x</code> can be represented as a limiting case of the interval <code>[x,x+h]</code> as <code>h</code> approaches <code>0</code>. The measure of the point, <code>(x+h) - x = h</code> as <code>h</code> approaches <code>0</code> is therefore <code>0</code>.</p> <p>However, if we take a line segment--say, <code>[0,1]</code>--and decompose it into <code>n</code> intervals <code>I[k]</code> with <code>k</code> being over the integers from <code>0</code> to <code>n-1</code>, each will take the form <code>I[k] = [k/n, k/n + 1/n)]</code>. If we let <code>n</code> go to infinity, each of the <code>I[k]</code> can be modeled as a point because <code>1/n</code> is approaching <code>0</code>. If we take the measure of each point, we get <code>1/n</code> as <code>n</code> approaches infinity, or zero. On the other hand, if we sum the measures of the points, we get <code>1/n * n = 1</code>, the measure of <code>[0,1]</code>.</p>