TADM2E 1.17

<b>Step 1:</b> Show that the statement holds for the basis case <math>n = 1</math><br>

<math>E(n) = n - 1</math><br>

<math>E(1) = 1 - 1 = 0</math>. A tree with one node has zero edges

<b>Step 2:</b> Assume that that summation is true up to n.<br><br> <b>Step 3:</b> Show that on the assumption that the summation is true for n, it follows that it is true for n + 1.

<math>E\left(n + 1\right) = n + 1 - 1</math><br>

<math>\Leftrightarrow E(n) + 1 = n</math> When adding one node to a tree one edge is added as well<br>

<math>\Leftrightarrow n -1 + 1 = n</math><br>

<math>\Leftrightarrow n = n</math><br>

QED