Discrete Math Proofs in 22 Minutes (5 Types, 9 Examples)

We look at direct proofs, proof by cases, proof by contraposition, proof by contradiction, and mathematical induction, all within 22 minutes. This video includes 9 examples: 3 for direct, 2 for proof by cases, 1 for proof by contraposition, 2 for proof by contradiction, and 1 for mathematical induction.

#DiscreteMath #MathProofs #Proofs

0:00 Proof Types
3:00 Direct Proofs
9:04 Proof by Cases
12:30 Proof by Contraposition
14:05 Proof by Contradiction
18:00 Mathematical Induction

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[minemanfan]

What convenient timing!
My discrete math final is literally tomorrow!

[ssleepyss]

Respect from Kazakhstan, I am a freshman at Kazakh-British Technical University, and you help me a lot with your videos about discrete mathematics ❤

[RedFidgetSpinner-rb]

I'm currently studying Discrete Mathematics right now on my own. These proofs are a good summary of what I've been doing. Right now I'm working through the How To Prove It Book by Daniel J. Velleman. I find your channel to be very helpful. Thank you for your videos!👋

[meead]

you just saved me a lot of time. Thanks mate!

[WomBComB_x]

Convenient! My discrete math final is in 4 days :O.

[willpage]

This was great review before an exam THANK YOU

[MrBartusek]

some of your proofs are too hard to follow man, too many shortcuts for mere mortals

[anjolasigbeku]

Binge watching your videos before my Discrete math final in 4 days. Hopefully she goes fine.

[jong.]

Look at this guy, it's like he has a timer for these things.

[Yohan-qewr]

In the first example of proof by contradiction, "If a is rational and ab is irrational, then b is irrational"
Isn't starting with the assumption b is rational and coming to the conclusion ab is rational instead of irrational, same as proof by contrapositive?

a is rational and ab is irrational -> b is irrational (P -> Q)
b is rational -> a is rational and ab is rational (NOT Q -> NOT P)

[yeaman]

Amazing. So much easier to understand than my foreign professor can't speak English properly

[zohairrasheed]

Would an If and only if case require a proof by contrapositive and a direct proof?

[GoroGoroGoroChan]

still kind of confused. How do you assume or find what to find? And for question 2 I still don't understand why root x<= root y becomes x -y or how we get (root x - root y) (root x + root y) <= 0

[AE-ixiz]

7:07 I’m confused that question says “show that for x and y are positive numbers..” but you wrote “x - y <= 0”. Isn’t a positive number supposed to be written as “x - y >= 0”?

[joshe]

isn't base case for last example n = 1?

[Boogi-]

Why the FUCK I am learning this as a cs student

[magicmaddox]

good video but Im ngl idk how you proved these, If you could show your answer actually works that would be great. For a^2 not divisible by 4, if you could show how your final proof actually proves it is then that would be great.

[calculadwest]

In last example I can't see why you just stated that k>1

[Yoursoul]

At the last one, why can we say 2^k*2>2k? why can't it be just 2^k*2>k