math-complete-induction.html


* created: 2025-05-19T21:41
* modified: 2025-07-03T08:52

title

Complete Induction

description

The principle of complete induction is used to proof a logical for all statement. This is done by showing that there is at least one element for which the statement is true and then showing that this is also the case for $n+1$.

Staying true to yourself at all times

  1. Define a generell for all statement which we want to proof.
  2. Base Case (Induktionsanfang): Show that there is at least one element for which the statement is true.
  3. Hypothesis (Induktionsvoraussetzung): Go with the hypothesis that the statement is true for n+1.
  4. Inductive step (Induktionsschritt): Show that A(n) \Rightarrow A(n + 1).
  5. Conclusion (Induktionsschluss): As shown in the steps above n=n+1 ; therefore we can conclude that the statement is true for all elements.