❖ Proof by Induction ❖

Understanding Proof by Induction: Step-by-Step Guide to This Essential Proof Technique

In this video, we'll explore the fundamental proof technique known as proof by induction. I'll walk you through how to construct the basis step, where we establish that the statement is true for an initial value, and then move to the induction step. In the induction step, we'll assume the statement holds for some value of 'k' and demonstrate that it must also hold for 'k + 1'. This powerful technique is widely used in mathematical proofs and is crucial for understanding deeper mathematical concepts.

What You Will Learn:

How to perform the basis step in a proof by induction.
Constructing the induction step and making the appropriate assumptions.
Applying the method to demonstrate that a statement holds for all natural numbers.
Examples that illustrate each step of the process.
Insights into why induction is a powerful and widely used proof technique.

📚 Check out my book: 1001 Calculus Problems for Dummies for more practice!

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[CleverProgrammer]

I watched multiple other videos, read other textbooks, listened to professors, read blogs, listened to a podcast, and tried some other mediums of learning as well to understand how inductions work. This video was the best of all and ONLY one to help me get it, bar none. Thank you.

[bobba]

Whenever I don't get something, I can these days guarantee that Patrick will make me get it.

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[rosemarypatronellamatura]

i never understood induction forv the pst two years in advanced level and i avoided those questions at all cost .unfortunately wen i came to university i met INDUCTION but 1 hr on youtube with you changed everything.that was great.i like proving by induction now .thank you keep it up

[lovehearts]

Learned this in high school: didn't get it
Learned this in college summer class: didn't get it
Learned it in normal college semester: didn't get it
Stumbles upon a 6-minute Youtube video: GETS IT.

[israelfailin]

Alright, I get proof by induction now, thank you. Guys, is there anything more painful than reading a discrete math textbook?

[PersuasionBlasian]

You sir have taught me in less than 10 minutes how to do something we've spent hours in class time on. Thank you!

[swaysway]

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[stephenmack]

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[coffeeagent]

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[MrMeagain]

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[konflictification]

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[TheIdontwannadothis]

I have been trying for hours and hours to understand induction, i watch your video and understand in 6 minutes, 29 seconds how to use induction. You are incredible, you are times better than the TA's at my university. Thank you so much.

[callofdutyman]

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[Kurogames]

Oh god, I can't thank you enough for this bro. I've been trying to understand how to do this for almost a couple of months now, and nothing ever worked. The material provided by the teacher was confusing, the written material online confused me even further, but this, this just clicked. Thanks a lot.

[kurchak]

By the way, my university's official course content links to this video in its "Proof Techniques" lesson. And it's an ABET accredited Computer Science course (Algorithms and Analysis). And I don't mean like the professor said "hey check out this video", no, it's actually in the official published material lol. And they link to you! I think that is something to be proud of.

[TakeItEasyC]

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[danamuise]

You helped me get through pre-calculus with this video years ago. Now I'm in discrete math, learning proofs, and here I am, back again!