Step-By-Step Guide to Proofs | Ex: product of two evens is even

How do you prove a mathematical claim? This video provides a step-by-step process to help you prove simple, direct proofs. We begin with the assumption, apply the definition, do some manipulations, apply the definition of the conclusion, and finish at the conclusion.
We will investigate the claim "the sum of two even integers is even" as a template for this proof style.
Learning Objectives:
1) The four major steps in proving a theorem
2) The give details that occur in the body of a proof
3) The rational behind the various steps in our first formal proof.
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[@russ5943]

You deserve a percentage of the tuition paid by every student in every discrete math class ever. When people ask me who taught me discrete math my answer is "Trefor Bazett."

[@KristoKorps]

I really appreciate this video and the way you went about breaking things down into steps. My discrete math class is currently way too fast paced for my learning style and this in-depth thought process forming breakdown is exactly what I needed. Thank you so much and keep up the great work!

[@rapidreaders7741]

And the fact that he had to write _everything_ backwards so that his viewers could see it.

[@shubhamsatyaprakash54]

@@rapidreaders7741 he writes in a natural style and by the way he is right handed. He make these kind of videos possible by certain softwares and flips the writting style

[@DrTrefor]

Glad it helped!! :)

[@rileymaas1068]

Thank you so much, I'm a computer science major and this really isn't what I signed up for, so I really appreciate the help. You make this information way more digestible than my professor haha

[@zainahmed6502]

Doing problems like these will help you improve your algorithmic skills in long term, trust me. Computer and programming logic structure is completely based on the principles of Discrete Mathematics.

[@C.r.i.m.s.o.n]

100% relatable

[@twonulator]

The way you break down and label the proof as a symmetric "sandwich" of structural sentences was excellent insight. Big lightbulb moment. Thanks!

[@DrTrefor]

Glad it helped!

[@laurabruges5820]

¡Gracias!

[@laurabruges5820]

Sorry, this has been automatically posted, I cannot express how grateful I am to all what I've learned from seeing your videos. I'm a software developer looking forward to straighten my basis on computer science, and your videos have made me stop fearing math and formal definitions! Thanks a lot Prof., I hope I'm able to complete the whole series real soon!

[@joshman1019]

This is by far the hardest class I've ever taken. I just cannot wrap my head around it. Granted, my problem sets are not this easy to break down. So I'm still stuck. But this helped.

[@DrTrefor]

It really can be hard at first. Stick with it, it gets better in my experience!

[@sweetlemons8695]

I'd been lost in my proofs class for days, and came to KZbin out of desperation; this was such a big help! Thank you!

[@ericfricke4512]

These videos are the reason I will pass Discrete Math this semester! Thanks for sharing your knowledge in a crystal-clear manner!

[@jyke321]

Logic makes a lot of sense to me, probably cause I've been fiddling with for a long time while trying to make games, but proofs have by far been the toughest part of discrete math so far. This video helped a lot, but I still struggle in the playing around phase that I hadn't even realized existed. This video helped a decent bit, thanks.

[@Gaylord69420]

Question, how did you learn it? Do you have a textbook?

[@marcusaurelius2147]

My late blooming love of physics got me to sign up for university in my late 20's, little did i know that abstract linear algebra was on the menu. Now i'm banging my head trying to prove operations in the coset of W containing V. So its back to the basics with evens and odds, trying to understand the mental gymnastics one performs to prove something in the mathematical sense, and on that point your videos are a great resource.

[@user-qy6tu9ip9v]

I haven't started engineering yet but I know this is going to be rough.

[@justinmeyer8046]

Dr. Bazett has been my saving grace. My lecturer has no clue how to present Math in general

[@jonellpadongao7370]

As a way of appreciation, I never skip any ads. Thank you very much, sir.

[@mendelovitch]

Love makes one want to shout it from the rooftops, or on KZbin. This man truly loves maths.

[@williamwalker1521]

This is so helpful! Writing proofs is by far my least favorite part of discrete math, and you've really broken it down so it makes sense! Your videos have helped me drill down concepts so much!

[@hunter9035]

This guy is such a professional he can write backwards on a piece of glass

[@monkeydonk3925]

I think he probably writes forwards and then flips the video in editing so it's the right way round for us? I don't really know that's just an idea

[@chloecheung7690]

This video was extremely helpful!! I was struggling with the format of proofs but this video had everything I was looking for. Thank you so much!

[@serenaaaa1337]

This is definitely helpful and a very organized way to interpret proof techniques. Very appreciated!

[@phantasqLiving]

Wow. Commenting on this to internalize. Phenomenal.

[@GrahamCrannell]

7:57 - "fuck around and find out" is the backbone of all research 😅

[@Kaizen01395]

I love math a lot, but for whatever reason discrete math was difficult to understand, but I just solved the problem before watching this video and followed the 5 steps from the last video and it's SO EASY. I'm not sure why I didn't understand this in class. Do you have any videos explaining the Pigeonhole principle?

[@ashIesha]

thank you so much for your videos !!! i’d lay you my tuition myself if I could

[@thaniacisneros5785]

Thank you so much for all your videos! You are making my life easier!!:)

[@etimezz]

your playlist > my discrete university course

[@PANKAJYADAV-iw4kz]

Watching from India 🇮🇳 at 1:35am in search of joy

[@MagnusTheUltramarine]

in 6:16 you could have written: n is even For all k in Z such that n = 2k instead of "there exists". After all any number k in Z times 2 is even Is this correct?

[@mdgulamgoash7560]

n=2k ; this statement is true not for all k in Z, but true for some specific k in Z.

[@MarianneGraceGamurot]

big thanks for this, it helped me a lot.

[@Gratitudeprayer]

Thanks a lot ! your teaching is very great !

[@zainahmed6502]

I wish I could direct my tuition money to you instead of my professor!

[@elfentsuki]

Excellent video!! And love the energy, thank you so much for this video.

[@nanu4144]

Could I define an even integer as something that is divisible by two and left with no remainder?

[@MuhsinFatih]

Exactly what I needed. Amazing guide! Subbed

[@sarkersaadahmed]

15:23 why dont we use contradiction rule because not only even * even is even but also even * odd is even

[@guyblack9729]

P is stored in the integers

[@Hafsah-t6f]

ahhhhh thank you thank you thank you thank you thank you!!!!!!!!! thank you!!!!! thank you!!!!

[@davidlasry3559]

Wow! Great video, thank you

[@khaledfarrag9754]

wonderful effort

[@dulakshivitharana9007]

Thank you so much sir

[@nekomaru3679]

I cannot see the step 4 at the end as it is covered by your playlist on the video...

[@leonardomorel9412]

Dr.Treffor = Suppose m and n are integers Me = no they're chocolate

[@DrTrefor]

I WISH

[@TheAdrenalineJunky]

Is the recursive nature of the proof useful or relevant? Ie mn=2t. If you recursively apply the proof to 2t, eventually you get 2*2=2*2?

[@NathanStraub92]

Thank the Lord for KZbin.....I would be a lost cause otherwise haha

[@5Stars49]

QED means ???

[@alainsavard8373]

Q.E.D. (quod erat demonstrandum), used at the end of a mathematical proof. Meaning "that which was to be demonstrated"

[@TheMacTownPoke]

Excellent teacher

[@velaabiss4531]

Can u pls show us how we prove that an equation is composite.

[@ErgunPascu]

This is so cool.

[@shielacarilo2595]

Thank you so much sir😊

[@marcusofranz1102]

I don’t understand why you don’t need to prove that an integer times an integer is an integer or state it as an assumption. How do you decide what the reader is to infer, vs what your are explicit about.

[@sarkersaadahmed]

how in the world does my channel know that I am watching discrete maths and pops up an advertisement on discrete maths

[@arpanpain4439]

the formal definition of the even numbers should be like for all k in Z , n = 2k isn't it?

[@embracinglogic1744]

@@DrTrefor You are correct. You should not say almost, you should say wrong. The way he words his definition is completely wrong. Your definition is exact and thus correct. Preciseness and formality are fundamental in mathematics.

[@oczar9779]

Good teacher, I just think that this could be dumbed down some more

[@justaperson4242]

What is the mirrored E?

[@dm7893-p2t]

“There exists”

[@yunoletmehaveaname]

Is it satisfactory that 2rs isn't proved to be an integer?

[@moustafafarag3658]

great video but at 14:36 shouldn't the algebra part be 2(rs)?

[@JohnMuller]

This confused me as well at first. But if you think of it as (2r)(2s) = 4rs, you could then break down 4rs into 2(2rs).

[@semhararadom1491]

Perfect

[@saif0316]

thank you so much!

[@goatfishplays]

For the "for all m,n in integers" at 5:54 should the integers be integers^2? or is that just for vectors and stuff? also for the format at 7:04, does the "For all x in D" part matter? in video 29 of your playlist didn't it get stated that the P(x) => Q(x) means "for all x in D, P(x)->Q(x)".

[@barlerer]

Are you writing backwards or is this some video editing dark magic?

[@OfferREI]

@@DrTrefor I was wondering about this! This is the best format I have seen for teaching math

[@magnetsec]

Write normally on a glass, flip the video, then edit on top

[@ilikewaffles3689]

I don't get it. It seems like circular logic trying to prove what even numbers are by using even numbers in the proof.

[@criticalsting]

Not all heroes wear capes

[@_ramen]

Suppose eminem are an even integer.

[@RemotHuman]

Title should be product of 2 evens is even

[@DrTrefor]

I'm kind amazed it took 28k views before someone noticed this lol! Fixed:)

[@GuidoHaverkort]

Does this guy just casually write mirrored?

[@DrTrefor]

haha, either that or I flip it on my computer afterwards:D

[@hoppinnoppin8110]

Huh

[@lbierman]

Could you present this with less verbage. I may be a dog because all I hear is blah, blah. Why is a proof so difficult to explane? Twelve minutes in before you get to the first line of the proof, and you have confused me thoroughly with asides and an assortment of what seems to be an endless supply of mathematical symbols. Please, simplify and leave out all asides.