math-induction.html
* created: 2025-05-19T21:41
* modified: 2025-10-28T15:57
title
Math Induction
description
The principle of 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
Define a general for all statement which we want to proof.
- Base case (Induktionsanfang): Show that there is at least one element for which the statement A(1) is true.
- Inductive hypothesis (Induktionsvoraussetzung): Go with the hypothesis that the statement A(n) is true.
- Inductive step (Induktionsschritt): Show that A(n) \Rightarrow A(n + 1) with the help of the inductive hypothesis.
As shown in the steps above A(n) \Rightarrow A(n+1); we can therefore conclude that the statement is true for all elements.
Peon Axiom
TODO!