In this video, I discuss a powerful method called **mathematical induction**.

Hi, I’m Dave, welcome back to my channel.

In this episode, firstly, I’m going to work through several examples that demonstrate how to use induction. I’ll also talk about the Well-Ordering Axiom and Strong Induction. After that, I work through several more examples, I prove that the Well-Ordering Axiom, Induction, and Strong Induction are all logically equivalent.

Before you continue, download the video notes here: Mathematical Induction pdf notes. You may also be interested to know that this video is part of the Number Theory Series playlist.

## Mathematical Induction (With Lots of Examples)

### How-to Learn Mathematical Induction

Induction is challenging, especially for beginners. That’s why I made this video so you can become skilled.

#### Total Time Needed :

82

Minutes

#### Total Cost:

0

USD

#### Required Tools:

#### Things Needed?

## FAQ Mathematical Induction

## What is an excellent mathematical induction example?

Mathematical induction allows us to prove statements that depend on a natural number to be true for all natural numbers. For anyone to accomplish an induction proof, a base case and an inductive step must be justified.

## Is mathematical induction challenging?

In general, learning how to write proofs is hard, especially mathematical induction. Proof by induction is typically hard to understand because of the inductive step, requiring a student to make a hypothesis, deduce a conclusion, and then conclude the proof.

## Why do we use mathematical induction?

People use mathematical induction because it is potent. To be able to prove a result (with infinitely many cases) correct is compelling. Moreover, once someone practices induction, it becomes effortless to use.

## How do you do strong induction proof?

Strong induction is very similar to mathematical induction; however, the inductive step is different. With mathematical induction, the inductive step is valid for a natural number implies valid for the next natural number. In proof by strong induction, the inductive step is the following: valid for the first consecutive finite number of cases implies true for the next natural number.

In conclusion, I want to turn it over to you.

**Does induction always have to have a base case? **

So, either way, let us know what you think in the comments of this video: Mathematical Induction right now.

## Related Articles

- The Best Facebook Pages for Mathematics (Who to Follow) - September 24, 2020
- The Best LinkedIn Pages for Mathematics (Who to Follow) - September 24, 2020
- The Best Instagram Accounts for Mathematics (Who to Follow) - September 24, 2020