Proof by Contradiction | Method & First Example
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- เผยแพร่เมื่อ 28 ส.ค. 2024
- Proof by Contradiction is one of the most important proof methods. It is an indirect proof technique that works like this: You want to show a statement P is true. First assume the P is actually false. Then manipulate until you get a contradiction like 0=1. This means your assumption that P was false is incorrect and so P is true. QED.
In this video we'll talk about the structure of proof by contradiction, and then do a small example where we prove a theorem that no integer is both even and odd.
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im not sure what to be more impressed by, how clearly he explained this in 9 minutes or the fact that he can write in reverse and make it look good
pretty sure he is just writing normally on the glass, but mirrors the video before editing it. unless he is also left-handed to prove me wrong :P
There is no way you can understand what he's talking about, yet be stupid enough to think he is writing in reverse lmao
I’m assuming he used a mirror
@@syndrac6254 where is your proof??? (by contradiction)
The contradiction (k1-k2) being 1/2 was such a subtle and beautiful point!
Ah yes. Graduated a few years ago with my math degree but still come here to pay homage. Thanks!
deadass you cleared up every question i had about this concept within the first two minutes. ur an amazing teacher
Catherine Dinh you gotta be from New York 🤣🤣 no one says, “deadass” except for us New Yorkers hearrddd
@@re-know251 lol
Bro taught me in 9 minutes what my professor just yapped from the slides for 2 hours. MVP
I sense both teaching skill and passion
and technology and thoughts and effort and post production
the videos my university class provides me are absolutely mind numbing, it goes such a long way to have someone energetic on the screen explaining this stuff
I don't know what's the reason but this video helps me more in understanding the lesson than my professor teaching this topic. Thank you for this educational video!
So beautifully explained. In grade 8, my mathematics teacher introduced us to this proof my absurdity for the first time.. and he was fascinated by it so much that i also fell in love with this technique.
Your explanation is appreciated by all. Love from India❤
Thank you Dr. Trefor Bazett and I am really enjoying your DIFFERENTIAL EQUATIONS playlist as well.
i swear from morning i watch a videos but i didn't understand any thing till i found you best dr. for ever from now i am one of your subscribers💌
This is so trippy! He's writing in reverse!
I think he mirrored it in post
But he writes "There exist like a normal E". 'Elk nadeel hep se voordeel.
look at his shirt the pocket is on the right side its mirrored
he isnt hes also right handed its mirrored in post
Sit, besides your mirror👍🏻😃
This guy is the PatrickJMT of higher level math.
I must say you are so dedicated to these videos that you write in reverse! well done
I really love your video, like it's way easier to understand than my prof's lecture tbh...
I kind of get how to USE all the proof methods, but how do people know which one to use for each problem??? Practice?
Thank you! It sort of builds slowly out of experience. It's a bit like chess, there are a huge number of moves possible but as you gain experience you'll see the best move in any given situation.
Perfect example to explain the topic! Thanks for the video, Dr. Bazett!
I usually do not write comments but I had to. You were awesome. Thank you so much. You deserve my like and sub.
Thanks my teachers goes way to fast and messes up a lot. This made it clear
This is worth listening to than the three hours of lecture of my Professor without actually explaining anything.
Wow, this video is amazing. The textbook I had to buy for my class doesn't even come close to explaining the concept this clearly.
yeah, school level textbooks are crap basically. written by bunch of jerkoffs
*Lots of love from India . Sir !! You are much better than my collage professor !*
Your teaching skills and writing skills outstanding . I have nothing word for your teaching .
Thank you so much 😀
This is the same example that the doctor explained to us in college 👍
thanks for this...its helpin me for my exam preparation
Dang man, they are still releasing DLC's for math? How much longer are they going to add to this?
I miss the old 1+3=4 game.
I love your passion sir and your videos are amazing
Proof by contradiction is basically another word for humor
Let n be the number of vertices of a graph G.
If G is a tree, then G has n − 1 edges.
The contrapositive of Theorem
Let n be the number of vertices and let e be the number of edges of a
graph G.
If e ≠ n − 1, then G is not a tree.
However, if e = n − 1, G not necessarily to be a tree.
(The converse is not necessarily true.)
How can i use contradiction theory to prove it?
Beyond excellent
Hi sir!
I'm from India.
🇮🇳
IS this universal modus tollens ??😩 Thanks for the clear explanation!
i like your explanation thanks a lot
Thanks for another helpful video!
Thank u so much Dr 😊 u explained so well 🤝
wow this video really helped a lot .. your the best
Nice explanation
And there was me thinking the important methodology was SHOUTING.
he made it so clear but at the same time I am confused
is he writing on a mirror ?? if so how is he writing it in the wrong way for us????
what's that symbol your are using as and AND in the sentence "n is even AND odd?"
The could have been proven the almost the same way but with a direct proof, right? First you rewrite the For All statement into a Not Exists and you take away the negation in the body. You then arrive at the same contradiction inside the body of the Not Exists. The exist turns into false but because of Not Exists it turns into true and now the left hand side of the original proposition is always true. Am I missing something?
Contradiction: 1 is an even integer since there exists an integer m such as 1 = 2m
What happened to De Morgan’s law while negating an and it becomes an or
this might be a dumb question....but are your writing backwards?
how does this work🥲
Great video. Shouldn't the contradiction be "N is even OR N is odd?" Because the negation of AND is OR? Or am I just being smallbrained?
Well, because it is a contradiction the negation is in front of the "for all" as Dr. Trefor drew. You can then move the negation that is in front of the "for all" inside the body of the "for all" to rewrite the universal (for all) quantifier into an existential quantifier. Because you moved the negation from in front to inside the body you get the following: negation-negation(n is even and n is odd). Now the double negations cancel each other out. You seem to try to reference De Morgan's law where Not(A and B) can be rewritten as Not-A or Not-B.
U
According to De Morgan's rule isn't the negation of n is even AND odd become n is not even OR not odd?
Oh you are right. Thanks!
Sir, thanks a lot
Thank you !
Didn't notice any Law of The Excluded Middle(LEM) jumping into the ring, but they are out there amongst the flat earth crowd somewhere.
Love From india❤
helpful video thanks man!
now i can proof that my friend cant identify as a toaster
LEGEND
Isn't 2(number) = 1 a contradiction because even != odd?
Yes
When do you use "such that" and ","?
Thanks! When I studied Mathematics in High School, back in Peru, we used this "/" to represent "such that" (tal que), in spanish). In one exam, here in the US. I used that symbol in an exam and my teacher wrote in my exam that she wasn't sure what I meant with that. and it was a "There is " statement.
Great videos, bu the way. It is easy to follow your explanation.
im on step 2 all the time
The real question is how did he write on the board like that?
great!! Thanks!
I want you to be my teacher huhuhu
so proof by contradiction is trying to make an insane argument that could never be true?
well this is gonna be easy.
Use white colour. As chalk colour
Fun fact: a reduction is actually a proof by contradiction, but not the other way around
now wheres the proof of : diff of 2 integers is an integer :thinking:
this exercise is left to the viewer, hah!
@@DrTrefor you can only prove it by contradiction, showing that a number cannot be odd and even at the same time, lol. Kinda vica versa thing happens there.
Please let me know how to solve this question.
Translate the following argument into symbolic form and using rules of inference derive
the conclusion.
It is not the case that some students are not employees. Furthermore it is not the case
that some employees are not hard workers. Therefore all students are hard workers.
b) Consider the following paragraph:
“Anyone who has catarrh will sneeze. If anyone allergic to animal dander or dust mite
then they will have catarrh. Maya is allergic to animal dander”
(i) Write the above paragraph in first order logic and convert them in to conjunctive
normal form.
(ii) Using the method of contradiction check whether Maya will sneeze.
sir with u and your method is soooooooooooooo cute
Did you learn to write with left hand or you were born left-handed?
how tf can u write like that? wttff
he is so handsome 🥰🥰🥰
when did jacksepticeye make math videos
Please speak in hindi.
😂
Could have been simpler if you didnt bring the math inside it and had taken just a logical statement like the Earth is round or something along those lines...but thank you for the video...
Thanks..got it. My comment was more on non mathematical lines and later I realized my mistake on making this comment. This video is related to using the proof in the Math field. I was looking more for a generic explanation on the topic of Contradiction.