Intro To Math Proofs (Full Course)

[@BriTheMathGuy]

This course might have mistakes or define things slightly differently than you will/have seen in other texts. If you find an error please reply to this comment with timestamp. I will do my best to make corrections (in the video description or otherwise) with the tools youtube allows at the time.

[@christianpio1261]

At 59:55, the negation should be “m OR n are even”, applying de Morgan’s law, right?

[@ahmedhamdi9358]

@@christianpio1261 exactly that's what I was about to write.

[@timothymcglynn1935]

Thanks 👍

[@pc4shglitch746]

there's a typo of exists at 35:43 there's a typo of absolute at 39:10

[@kurtgodel5236]

1:00:00 The negation of a conjunction of two formulae is the disjunction of the negated formulae. That is ¬ (m odd ∧ n odd) is logically equivalent to (¬m odd ∨ ¬n odd). That's a logically weaker statement than (m even ∧ n even).

[@z.Cyanic]

0:00 What's a Proof 10:44 Logical Rules 17:38 Mathematical Sets 30:38 Quantifiers 41:50 Direct Proofs 52:35 Contrapositive 1:01:39 "If and Only If" 1:12:28 Proof by Contradiction 1:23:01 Theorems are always true. 1:27:48 Proof by Cases (Exhaustion) 1:38:56 Mathematical Induction 1:51:17 Strong Induction 1:54:40 Introduction to Function. 2:01:49 Existence Proofs 2:11:01 Uniqueness Proofs 2:18:22 False Proofs

[@GoGo-c7x]

.

[@brothercaleb]

god’s work 👏🏽👏🏽👏🏽

[@scottleung9587]

Thanks so much!

[@AbdallahAttiaA]

1:09:50 proof by contradiction

[@andrewg5672]

thank you for speaking VERY slowly and defining everything. Your pacing is excellent, and i LOVE that you constantly say "so what does this mean?". You are a true teacher who wants students to reflect and take a step back to digest and it is a very underrated skillset as an educator. A lot of math professors move too fast and automatically expect students to be at their level. They are great mathematicians first and educators second, which can make things greatly intimidating and disheartening for some students. Keep up the GREAT work!

[@starwaItz]

Was going to say this. We appreciate the pace!

[@Canda-fh4xc]

I wish I watched this video 25 years ago when I was in college. Your explanation is very easy and clear.

[@TheArtmatician]

I love you, man. Thanls for the almost 2h30min. I'm gonna do a very good use of them, don't worry.

[@Robert-er5wq]

10:30 That is what puts most people off: proofs that have been brewing for 2500 years in the heads of human kind are presented in the most slick way and as straight forward. I think one needs to make a huge disclaimer around that. Usually maths student start to prove the laws of set operations, because it is plugging in definitions. The genious spark comes later, after having seen A LOT of ways how to prove things.

[@PrimordiusDragon]

Hey man, I'm a freshman at Stanford studying math right now and this video has been super helpful! Just wanted to let you know that you're making an impact in my life (and likely my mathematical career). Thanks for this amazing video!

[@kaewoomusic]

colleges are charging thousands of dollars for a course like this while this guy is doing it for free

[@sumofat4994]

You can also buy books those are things too. Also in a course you get feedback directly from the instructor so its not really the same but still this is a great video which should always be complementary with a book.

[@Rikri]

I'd recommend checking out Book of Proof, which has a free online version

[@casualmetalhead9383]

@@sumofat4994exactly…

[@alphagamer7058]

not really the same thing. a face to face in class is way better, instructors responses you instantly when you ask during classes. you try to follow through the exercises, they can check them for you, feedback you, give you advices.

[@crix_h3eadshotgg992]

Lectures aren’t worth shit. I always learned best from textbooks and forum discussions on them. But I’m autistic so maybe you can extract meaning from other people’s words.

[@AbdulRabChachar]

Wow, I have recommended this video to my discrete mathematics course students... That's very helpful and to the point. ❤

[@Orillians]

THIS IS GOLD

[@shawonsarkar101]

this is the video that i have been looking since my high school days . it's a hidden gem 💎💎💎

[@syncradar]

I recently just thought of learning proofs, and it is here in my recommendations...

[@syncradar]

Alright, I subscribed.

[@tvesaatamannamohanty5948]

I dont even have words to thank you. You are great.

[@kellyandthehorses2877]

Why do I like this so much? Why does math work better for my brain with proofs?

[@JO-yq8fq]

I wish I could superlike this. This is great. Thank you for speaking slowly.

[@atharvbhalerao3062]

Love you bro! I wish I had found this before taking honours math classes in first year.

[@caliguy1260]

This is a great review. We did all of these techniques in my discrete math class, which was a really good comprehensive introduction to mathematical proofs.

[@Vengemann]

FINALLY SOMEONE GIVING PROOFS LOVE U BROOOO

[@ambermariemalone]

thank you for eliminating barriers to access for this information 🎊

[@katherinemarcelynalexander]

Suppose √2 is in Q √2 = a/b 2 = a²/b² 2b² = a² -> a = 2c 2b² = (2c)² 2b² = 4c² b² = 2c² -> b = 2d (2d)² = 2c² One must imagine Sisyphus happy

[@ChrisHamberg-ok2cz]

This isn't correct: 2b² = a² implies a = 2c sqrt(2b²) = sqrt(2) sqrt(b²) = sqrt(a²) implies a = sqrt(2) c

[@thehellfromthemountaint]

Yep, im gonna be a math major. Thanks, def helped me with figuring it out

[@boogie.devera]

Thank you so much. Your proofs are clearly presented.

[@FrancisZerbib]

The ultimate best math lesson on KZbin. I wish I knew even a part of it, while learning for my BSc. Thank you very much.

[@andresfelipe3081]

Thx man. I'm studying systems engineering and I'm seeing the discrete Math course. This helps a lot.

[@farzamimran3960]

I self studied proof by a book proof in math by richard hammack was a while ago so might have messed up the name but ur video is a goldmine for any new student .

[@joshuagalias9531]

This is exactly what I was looking for to review and prep for the fall. Thank you for the video

[@kenmeyer100]

A gem!

[@PrimordialOracleOfManyWorlds]

ultra-cool af math proving video. tyvm for me bringing back to the tautologies. i used to have a table or listing of all tautologies. they were fun to use in programming and proofs.

[@XtergoBlue]

I picked up proofs a week ago the timing was so good

[@kathlynarts]

Good Sir, THIS, this what I'm looking for!❤

[@scottleung9587]

This is awesome - it really could've helped me when I was taking modern analysis in college!

[@davethesid8960]

Be careful, in English the structure either-or IS exclusive. Btw, this was a great course, I really enjoyed it. Also, in Hungary 0 is considered a natural number.

[@hadibq]

I had "french typed" math education, and I really don't recall anything about the naming: Modus Ponens and Modus Tollens. While we studied the logical statements p-》q is equivalent to not q -》p. In programming, this helps simplify some complex logical expressions. Very useful indeed.

[@saidfarid6382]

Hello teacher Thank you so much for your interesting lessons, i do appreciate your job. I wish you peace and happiness under the sky of prosperity. All the best. Take care and have a good time.

[@niazghumro2350]

Nice video and this course should be offered at college level.

[@samiulalimsarkar5934]

Bro is serving to mankind. Brother really, thanks❤

[@masterweird]

POV: you bought the course on udemy and now find it free on KZbin💀

[@BriTheMathGuy]

You can request a refund:)

[@drka21]

​​@@BriTheMathGuyudemy has a proof that refund Is irrational

[@cambo-indiafriendship]

@@BriTheMathGuy its literally my class 12 maths syllabus

[@rajabfarooq8430]

Please make more comprehensive videos like this on various maths topic even if they are hours long

[@crowreligion]

5:21 I think you should first prove that square root of 2 exists in the set of real numbers in the first place To do this, you should define real numbers using cauchy sequences and come up with a cauchy sequence that converges to a number whose square is 2.

[@gmbachha6671]

You are the best youtube teacher I have ever Seem. Love from India ❤

[@SilentAdventurer]

1.5x speed works well 😂 On a serious note, great video!

[@pietersfilms5171]

Imma download this

[@СилвияБрянова]

I love, love, ❤❤ this!!!

[@superseondelight]

3:44 - Typo @ "Exisits" 5:13 - Typo @ "connot"

[@MultivectorAnalysis]

@59:55 the negation should be m odd or n odd, not m odd and n odd

[@Unknow5622-b1g]

Booooom 💪😎❤️

[@namangoyal1297]

This is so helpful!! I had a request though, can you make a video on strong mathematical tools which can be used in higher problems of physics, I was doing one problem involving black body which used riemann zeta function. That video will be really helpful

[@robertcampomizzi7988]

14:58 I remember my dad trying to use "non-exclusive or" to explain "or" in regular language skills to me as a kid 😂😂

[@florentikaa]

oh wow, how its working on you?

[@robertcampomizzi7988]

@@florentikaa I'm 45 almost now. Talking to peole in everyday life is hard because I don't know how regular people use words when they speak 😂😂😂 a blessing and a curse

[@adamczene]

What is this sorcery? Thanks❤ I was just searching on my PC how to prepare for math olympiads (wanna go to the IMO) and this popped up. ❤❤❤

[@pinkshortcomedy]

gl with the IMO!! im planning to go to the IPhO sometime and its nice to see another olympiad person here :)

[@adamczene]

@@pinkshortcomedy gl to you as well!

[@banrtv]

dope

[@whiteskybeats5534]

Dope Bro

[@qad1miy]

Thank you very much Continue )))

[@fredg.sanford634]

Thanks!

[@BriTheMathGuy]

Welcome! Thank you!

[@vancedforU]

13:27 Just nitpicking Here, the relation of q and r is not strong, maybe it would be better to say “People wear boots”

[@alikaperdue]

Why can't we notice that if n=2a+1 (odd) and then square to get n²=4a²+4a+1=2(2a²+2)+1, which is also odd and write this proof in a formal way @56:40 ? Update: I see that this doesn't prove that all odd n² have odd n. There might be an even n that squares to odd. I know there isn't, but I think the my given solution above does not disprove it, so the proof is incomplete.

[@abdulshabazz8597]

Hmm. So plainly stated theorem proving is an introductory course in first order logic. So if I can design an artificial neural network based Encoder based upon this principle which can distill Natural Language as human readable first order logic, which can be reasoned against by machines such as a Decoder this CODEC could be more powerful than any generative Large Language Model and may indeed demonstrate emergent behavior

[@ForStudying-w8q]

can u make a course like this for all international maths olympiad main topics. Such as combinatrics, algebra, geometry, number theory and other stuff

[@Escape_Model]

Thanks a lot .

[@danielrhouck]

Would it be possible to copy timestamps for when each episode starts into the description? That would let KZbin divide it into chapters, making things easier to follow. This is great but it would be better with the chapter divisions.

[@ghinahmaidosh5457]

But where did you use the assumption "M over N is a reduced fraction" in your first proof? I mean for it to be denied you need to use it some where in the proof at first don't you? For me, you prooved that the square root of two is a rational number that can be written as a not reduced yet fraction Please can someone explain so i can continue the video?

[@Kaurenjalalifarahani]

After a breakup i lost my purpose in life , still sad but math gave me a purpose

[@easymathematik]

Great video. Some points you could talk about. :) Often I miss the motivation to use a proof by contradiction. Why is this road a promising drive? For example for sqrt(2). Why is assuming sqrt(2) IS rational the way to go? :) This small detail would complete your great video!!! Keep it up. I follow your videos a couple of years already. :)

[@ssaamil]

Oh, these are from the udemy course :) btw do you plan to solve those interesting or difficult integrals again? they were pretty fun!

[@BriTheMathGuy]

That's the plan!

[@ddw1518]

hello sir, thank you for your tutorial. May I ask why 5:46 there is a subtle and important definition of rational number which is m/n is a reduced fraction? I have googled the definition of rational number but it only states that "Any number that can be expressed in the form 𝑝/𝑞, where 𝑝 and 𝑞 are integers,"

[@wolfang08]

Ive always had a problem with the first proof about proving irrationality. What if instead of sprt2 you just out sqrt4 there instead. Wouldnt that just prove that 2 (sqrt4) is also irrational?

[@alexandrutanasa9824]

4|m² does not imply 4|m.

[@trendsacrossafrica]

Merci beaucoup ❤

[@timothymcglynn1935]

Thanks 👍

[@yishaieidelheit7421]

‏‪1:00:54‬ I think you have a mistake the Negations of m and n odd is the either of them is even but not necessarily both of them. Regardless I wanted to thank you for the video even though I'm familiar with the concepts you explain them in a very good way.

[@anthonyr.capellan3198]

QED

[@fiyanshuNahar]

Hi have u guys read jay cunning long form proof , any opinion?

[@ishayisrael8101]

59:57 it's wrong, the negation of "m and n odd" is "m or n is even". You even showed it in 32:51 A correct proof: Assume without loss of generalities that m is even then, m=2k for some k. Therefore mn=2kn (an even number) => mn is even

[@ManishKashi]

Thankyou From india ❤

[@mirthun1012]

36:38 can anybody explain why the ST shifted its place in negation..

[@MaxEditsSpore]

Can you make a video about defining x^A Where A is a matrix

[@casualmetalhead9383]

I just can’t fathom the contrapositiv proof… how do they correlate to each other??

[@smeargloid]

timestamps for myself: october 7th 2024: 17:45

[@abir_existz7325]

How the hell did you just get m is not equal to n in 55:27

[@Joshua-cd7it]

11:31 LMAO AHGAHGAGAGAJHAHA LMAO..... kmai

[@kurtgodel5236]

11:15 Conditionals are not implications!

[@greatguytv]

It's not a course it's like a it's a video. You could always get this stuff for free to book. Everything in college was always available in books. In college you are paying for commentary, ie coaching. It's hard to self correct

[@darqed]

really cool video but im on the side of natural numbers including 0 ;)

[@josiaphus]

You misspelled “argument” in the first slide buddy…just a heads up

[@pandabearguy1]

Will this course present a proof of the Riemann Hypothesis?

[@StefanodeAngelis-1300]

I have a proof but unfortunately KZbin doesn't give me enough characters to write it here. Also, if I were to reveal the proof, were would the fun be?

[@lukealadeen7836]

In first proof why cant m an n be even intergers meaning sqrt(2) is rational?

[@altagent3472]

Because we see that since m^2=2n^2, m is twice another integer, the definition of an even number. Finding n to be an even number as well comes from the fact that m is even, as he showed, and is the contradiction.

[@kurtgodel5236]

2:18:22 There are no "false proofs". Speaking of a "false" proof (or a "true" proof for that matter) is committing a category error. Proofs are either valid or invalid. None of them are true, false, sweet or yellow.

[@usercommon1]

Спасибки❤

[@chadchiasson5724]

Big bang bust universe in a bottle

[@Chiavaccio]

👏👏👍

[@kioselnelio4598]

>no timestamps

[@pendragon7600]

>choosing beggar

[@amoghopprasad8286]

why does this video have just 5k views

[@mathematicsreligionandscie4322]

@12:32

[@OpPhilo03]

Please sir, Add Hindi language Audio track.

[@MadhukarKumar-ke6gd]

Could you do all the stuff for high schooler I am indian means from class 11 and 12 😊

[@piyushgupta_5647]

Hello 1st Comment Mathematics lover ❤

[@RZnisLive]

I hate conversly

[@worldnotworld]

"argument," not "arguement" 🙂

[@BriTheMathGuy]

I won’t argue :)

[@danuvab]

someone once asked me that what is the difference between a mathematical proof and logical proof? I gave him a logical proof of 0/0=1.(May be this seem very hilarious)

[@bvzr3806]

why is it so complexed

[@JimFarrand]

Defining the Real numbers as "the numbers that can be written as a decimal" seems a bit fishy to me. You CAN'T write pi as a decimal. You can write some finite prefix of pi as a decimal. And you can define a process that will output successive digits of pi. But neither of those things are the same as writing pi as a decimal. Doing that would require infinite paper and infinite time, neither of which are available.

[@edercuellar2694]

Then just define the real numbers as the ones that be written as infinite decimals.

[@benshapiro8506]

is it my imagination or did u say "taken 4 granite" instead of "taken 4 granted"?