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!👋
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)
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.
What convenient timing!
My discrete math final is literally tomorrow!
Respect from Kazakhstan, I am a freshman at Kazakh-British Technical University, and you help me a lot with your videos about discrete mathematics ❤
Same thoughts!
I am from KBTU too, прикольно видеть что пол КБТУ на этом канале сидит))
Love your countries music!
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!👋
Amazing. So much easier to understand than my foreign professor can't speak English properly
Convenient! My discrete math final is in 4 days :O.
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)
Yeah, another banger
YOOOOOO. Timing impeccable.
thanks man
thanks man!
isn't base case for last example n = 1?
7:07 I’m confused that question says “show that for x and y are positive numbers..” but you wrote “x - y = 0”?
Hello! In that same problem, it says that x
Look at this guy, it's like he has a timer for these things.
Would an If and only if case require a proof by contrapositive and a direct proof?
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.
should it be: x= 2a for ALL a € Z?
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.
some of your proofs are too hard to follow man, too many shortcuts for mere mortals
This is good review, but it would be good to have a video where you explain each assumption, operation, or each intermediate steps you skipped.