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.
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 :
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.
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