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
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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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[@minemanfan409]

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 ❤

[@alidarpanaguzhiyev885]

Same thoughts!
I am from KBTU too, прикольно видеть что пол КБТУ на этом канале сидит))

[@RedFidgetSpinner07-r5b]

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!👋

[@WomB0ComB0_x]

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

[@NoteNirvana.]

YOOOOOO. Timing impeccable.

[@AMIR-su4mc]

thanks man!

[@gaeel_]

Yeah, another banger

[@itsZahid22]

thanks man

[@jong.4864]

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

[@zackariasstrindlund3474]

should it be: x= 2a for ALL a € Z?

[@user-vs8kx2yz8o]

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

[@Trevtutor]

You’ll be proving both P -> Q and Q -> P so you yes could do it with a direct proof and one by contra position.

[@AE-ix2iz]

7:07 I’m confused that question says “show that for x and y are positive numbers..” but you wrote “x - y = 0”?

[@alexmarsonin8928]

Hello! In that same problem, it says that x

[@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.

[@Yohan-qe6wr]

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)

[@MrBartusek]

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