# Difference between revisions of "TADM2E 1.17"

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

$E(n) = n - 1$<br>
$E(1) = 1 - 1 = 0$. 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.

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

QED