Intro to Sets | Examples, Notation & Properties

[@ThisIsntmyrealnameGoogle]

Coming back a year later to say that I passed discrete math with an A+ and am now a Teacher Assistant for it at my university!

[@Uwek212]

Congrats! :D

[@DrTrefor]

That’s amazing, well done!!!

[@punkrider8758]

Strong man

[@frosty4513]

congrats man

[@dandandandaaan22]

Congratulations Sir!

[@punkrider8758]

I'll leave this here in case someone needs it: ∈ - Element of ∉ - Not element of ⊂ - Proper subset of (A is a part of B but they aren't equal, as in B is bigger) ⊆ - Subset of/Every element of (Since all of the members of set A are members of set D, A is a subset of D. Symbolically this is represented as A ⊆ D. Note that A ⊆ D implies that n(A) ≤ n(D) (i.e. 3 ≤ 6).) ⊄ - Not a subset of/Not every element of |- Such that ℤ - Integers (A number which is not a fraction; a whole number. Whole-valued positive or negative number or 0. The integers are generated from the set of counting numbers 1, 2, 3, . . . and the operation of subtraction. When a counting number is subtracted from itself, the result is zero. When a larger number is subtracted from a smaller number, the result is a negative whole number) π - Pi

[@xnopyt647]

pi

[@etiennedegaulle3817]

Good man!

[@ΒασίληςΧρήστοςΣμυρλόγλου]

thank you.

[@d-dawg3568]

You're a lifesaver thank you

[@gdemrakul2824]

@asvo7777 the first one is just "subset" meaning all of the elements of of one set are on another set, but they could have the same elemtents. The second one is "proper subset" and it mean one set is a subset of the other but they are not equal (it has fewer elements)

[@Troglodyte2021]

You deserve more than KZbin algorithm thinks you do.

[@Ilovetwerkin]

You make this difficult course easy, thank you so much. Can’t wait till more people discover this channel.

[@DipsAndPushups]

He explains discrete math better than my uni textbook

[@Tabularasaaa]

I love how the videos are not long and boring . Good job 👏🏽

[@milkeles]

One thing that could confuse some people while doing proofs, that may or may not be mentioned in future videos is that a set can contain a single number {1}, but a number itself is not a set. {3} is a set, but 3 is not a set. And because of that 3 is not equal to {3}.

[@flavioZ80]

Thanks.

[@ThisIsntmyrealnameGoogle]

WAIT... so you can write backwards??? That's amazing. EDIT: After some deep and critical thinking, there is the possibility of this video just being in reverse. You're amazing regardless though.

[@anthonyaportela217]

@@DrTrefor I'm sad to realize that you aren't left handed :(

[@SiyiZhou]

I am so impressed by this trick.

[@TheMR-777]

It is "Mirrored" by the way :), Reverse means to play from end to beginning.

[@guyblack9729]

I spent good chunk of time going through the same thought process and worried that maybe I'm not quite smart enough for this yet, then I saw this and your other comment and I'm feeling a bit more hopeful haha

[@TheMR-777]

Making the video, and playing it in *"Mirrored"* mode, also shows how creative you are Sir :),

[@pocojoyo]

YEAH, BIT THE SOUND IS $#!++¥

[@blogintonblakley2708]

Just write backwards... :)

[@brettpaden5929]

I’m not sure if it’s mirrored, his wedding ring is on his left hand whereas it should appear to be on his right if it was mirrored.

[@soph2124]

im starting to study robotics and AI and you´re videos are literally saving my life. you explain SO WELL!!! i wish you were my actual teacher :' )

[@MostafaAdwan]

man you definitely killed it in this course, short very informative and simple much appreciated

[@marykougl9726]

I am a liberal arts math student and I wanted to thank you! Without your videos , my GPA would tank

[@christopherbarrett9900]

I just discovered your channel and I am already liking the teaching style and energy. Looking forward to the next videos!

[@slykid139]

You make these concepts so easy to understand. Thank you!

[@jenniferwilcox4529]

You are an amazing professor! Thank you so much for making the videos, I'm doing computer science but I'm feeling the pull to the "dark side" as well :)

[@ritageraghty4404]

I say the same about him.

[@CrashTheComet]

Gotta respect a dude that can write backwards that quickly

[@tsubasacatt]

Isn't he write normally and flipped the video? He is behind the glass

[@MahdiehErfani]

It was very good and you described this subject obviously. I have just started learning mathematics in English. It was satisfying .

[@tttggg63]

Amazing videos. Your teaching style is great, love the lectures. (2021)

[@DrTrefor]

Thank you!

[@PLP0321]

Thanks for breaking it down so well!

[@backoffer3228]

Gonna watch at least 2 videos of your course every day and leave comment on all of them.

[@hamsoon5]

Great content! Where can I find any examples to practice?

[@IndronilBanerjee]

What is the prerequisite of this course, Dr. Bazett?

[@DrTrefor]

Nothing in particular. Probably about grade 11 math just for the sophistication.

[@reyfortea6090]

Hi Dr. Bazett, Is this part of a larger course that's available online? It's been difficult finding an online discreet mathematics course taught by an educator who's also skilled in communication, but your videos fit the bill. Thanks for the help. Best, Rey

[@DrTrefor]

Hi Rey, I have an entire discrete math playlist on the channel, but that is all that is available at this time, there isn't corresponding homeworks or things like that.

[@matthewthehuman1744]

thank you, I really appreciate this class being here, I've tried to listen to the MIT course, but I seem to be much more able to absorb things with your pacing/articulation of the ideas.

[@DrTrefor]

Glad it’s helping!

[@DanaNourie]

What text is recommend for this course? I’m not seeing mention of it. TY!

[@languagebattr]

No disrespect, I just need to get this out my psyche so I can concentrate... Hopefully. How does someone resist falling in limerence w/ you? I'll simply do my best Professor.

[@derrickchronicles5627]

Wow!!! You made it easy to understand.

[@DrTrefor]

Glad it was helpful!

[@GoutamDAS-ls1wb]

Professor Bazett, I am very grateful for these excellent series of lectures. I am using these to learn Real Analysis on my own as a number of topics overlap. As regards repetition of elements in a set, what about outcomes of rolling a regular dice X6 times? Then if I get 3 four times and 6 twice, then shouldn't the set contain 6 elements because each of these are results of a separate tossing? Granted then the outcomes would need to have superscipts or subscripts to denote outcome number? I guess in the latter method it would be a set of "ordered pairs" instead of just a "set".

[@nekomaru3679]

I'll take discrete math next semester... Thanks for making this!

[@Carauuhz]

how are you writing backwards

[@alaaadil6347]

is that full course or just basic and general info?

[@newtonthesecond9440]

can we appreciate how effortlessly he can write inverted

[@AdMrAuZmImNeGr]

I think they probably just inverted the video.

[@erickchavez1172]

First of all, thank you for this content, it is very clear.

[@Rogue_Art]

Hi Professor, are there any problems sets you have/recommend for this course? I saw your comment about the open source discrete math textbook and the online question submission system looks pretty interesting although it'd be nice to have some more complex problems as well :D

[@markpraire2572]

Do you have a recommendation for data structures and algorithms as a follow up after this course?

[@markgoldstein]

Thank you for these thoughtful videos.. I will go through all of the material

[@nasirmehmood8057]

Best lecture👍🏻

[@khalilmohammed2297]

thank you and i have a question why we use equals to beside the sign of subset why don't we use the sign of subset only

[@재준김-l4s]

Thank you so much Dr. Trefor Bazett

[@IamJacksHeartCA]

Is it more appropriate to use the proper subset symbol when saying that even integers are a subset of integers?

[@sunghyunpark2055]

Have one question. Per the lesson, the repetition does not matter in the set. Then, is {1,3,3} is a subset of {1,3,4}? And what text should I buy and read for this course as you mentioned in the first video of this course?

[@Rogue_Art]

Yes, {1, 3, 3} = {1, 3} which you can see is a subset of {1, 3, 4}. Writing it like {1, 3, 3} or {3, 1, 3} just makes it harder to see that one is a subset of the other. Generally this is why we like to have sets in either descending or ascending order and not have repetitions.

[@shalinmistrybca6636]

hello sir , do i need to only understand discrete maths concepts or practice as well coz i dont want to give any maths exam but i just want to be a good programmer . reply plz

[@romanrobinson1860]

I am just noticing that you use your left hand... Me too... I am loving the content btw, I am not learning a thing in my Discrete Mathematics class.

[@mkli3459]

If put so much effort to create a huge course, why to forget the sound quality? Thanks for the "echoing" experience. A tip for the next shopping list: a headset with a mic

[@luffyyyop3778]

are the notes available or i gotta write it down?

[@mostafaben3517]

if A and B had the same exact numbers, would it still be considered a subset? So would A = {1,3,4,7} be a subset of B = {1,3,4,7}?

[@JorgeGonzalez-kg4kn]

From what I understood of his videos. Yes A would be a subset of B. As long as every number that appears on A also appears on B it will be a subset.

[@moonstrike100]

YOUU ARE THE BESSSTTTT!

[@DrTrefor]

Thank you so much!

[@4xsin]

best professor ever

[@mathematics7331]

thank you for this, now i will proceed to the next video! (april 13, 2022 )

[@khalilmohammed2297]

Please this Subject is really important, could you make more about it. Thank you so much

[@cesareborgia7689]

I'm gonna come back to this later when I get a discrete math book

[@fubarace1027]

You are really really good at writing backwards, did you go to school for that? =p

[@DrTrefor]

Years of advanced training!

[@ZdenoMucina]

very helpful :) thank you for your teaching :)

[@Dazzer1234567]

Your videos are really useful, but you really need to work on the sound. First, you need to use some kind of microphone that clips on to your collar. That way, because your voice will be so much louder in the recording, you'll have much less room sound in your videos. Secondly, you need some room treatment. A good start would be lots of fabric (curtains). But this will only take care of the really high frequencies, there will still be some residual boominess. For this, you need some acoustic panels that contain thin rockwool or similar, placed strategically around the room. Also just more furniture, bookshelves, anything like that helps. That room you're in sound likes it totally empty! Check out the videos by Mathtutordvd, he's got a good sounding room in his videos!

[@Dazzer1234567]

Nice!...... after i wrote it i checked out some of your other vids and i see some are indeed better, but i still think they're all (at least the ones i checked) too boomy and room-soundy! The average viewer with no technical understanding won't be consciously aware of it, but they're likely to find the videos more fatiguing to watch because of this. I think this is really a key thing about making a successful channel, almost as important as the visuals. I also notice that you talk really loud (i think you've just got a naturally loud voice and talking style), but if you upgrade your gear (clip on mic), you might also want to experiment with talking a bit less loud, as a loud voice tends to "excite" boomy room modes more than a quieter one. I also find your loud voice a bit fatiguing and i would imagine it might also be less fatiguing to make the films talking less loud! Feel free to delete these comments, i won't be offended!

[@samarhadou7992]

What is the textbook that you recommend to students while taking this course?

[@DrTrefor]

I like this free open source one: discrete.openmathbooks.org/dmoi3/

[@fsaforosaforo6338]

Great videos, wish I had found them when I was taking this course twice.

[@nullbeyondo]

Can a set be a subset of itself?

[@DrTrefor]

yes!

[@ahmed735788]

you are awesome :) u deserve more subs

[@gdbku6600]

dude is writing backwards or just flipped the video

[@DamienRoyan]

Could be flipped. Is he known to be left handed?

[@alexrandall8557]

@@DamienRoyan Surely flipped, right? His breast pocket appears to be on the right hand side, which is possible but very very unusual for a standard button up shirt

[@duckyoutube6318]

Its on a mirror.

[@thodorisevangelakos]

Take a wild guess

[@curtpiazza1688]

Great intro! 😂

[@eny1103]

Is {1, 4} a subset of {1, 2, 3, 4} ???

[@DrTrefor]

Yup!

[@eny1103]

@@DrTrefor That was one quick response, thank you.

[@DolaLado]

Thank you.

[@javaexpertsa8947]

Is your playlist in the right order?

[@ycombinator765]

you looking young here sir!

[@stewedyeti]

I think you're a genius simply because you can write all of this stuff backwards.

[@kebman]

When typing, I think a solution is to use the exclamation mark as a symbol for not. So !∈ would mean _not in,_ or not part of whatever set. (I'm using Unicode Math in Sublime for symbols, but yeah, sometimes typed glyphs are a bit lacking as far as expressionability goes, especially when it comes to fractions, so woe to me for being slowly forced into LaTeX...)

[@davidlunacruz1150]

thank you!

[@stevenshrii]

Ln (-1)/ sqr (-1) = pi

[@nasirmehmood8057]

👍🏻👍🏻

[@sahajdeepsingh8779]

Him writing backwards is amazing…

[@yvng4697]

the vid got inverted

[@markmtz95]

I'm taking this class this fall and I don't understand anything. I'm scared that I'm not gonna pass this class.

[@luisriveragonzalez9052]

How did it go? I start this class in the fall. I am hoping I can study it in the summer :(

[@jinxscript]

wait a little bit of physics how is it that it is not leterally inverted 🤔

[@codatheseus5060]

I thought that element of symbol was the logic symbol for "there's atleast one way this can be true" like the opposite of "if and only if"

[@noha8235]

Shout out to all career shifting human beings🎉🎉 we can do it !

[@ElizabethKioko-r9w]

Any financial engineer hear 🥺(2024)

[@mrboyban]

Hold on a second! You sound like the Wall Mart announcer, is that you?

[@alexisk5978]

I will be back in December and I will pass Discrete math(manifesting)

[@DrTrefor]

Looking forward to your comment at the end of the playlist:)

[@isackdudiondiek8916]

Watching this video today January 2021

[@navjotsingh2251]

Not directly related to discrete mathematics, but this book is a good introduction to differential calculus for computer science students: www.math.ubc.ca/~feldman/m101/clp/clp_notes_100.pdf#page0 I like the approach used here and it introduces you to concepts without assuming you’re already a mathematician, it makes it a bit more sane to study haha

[@navjotsingh2251]

Here is the integral calculus book: www.math.ubc.ca/~CLP/CLP2/combined_clp_2.pdf

[@deansolistino]

Hey-- THANK YOU: this book is great

[@charlieb8735]

I just now realized he flips the video to write on the glass properly. Sorry to any lefties disappointed by this comment (As evidence, the buttons on his shirt are flipped)

[@yvng4697]

3/11/2022

[@cesareborgia7689]

3 mins in I rewind video

[@moter2179]

I thought you pronounced bag as BAAAG and thought you were midwestern

[@insightcody4213]

i think you are in a cave. . 😂😂

[@franccci]

Why is he kinda hot

[@chowdhuryazmalhossain8361]

Thank you, I really appreciate this class being here, I've tried to listen to the MIT course, but I seem to be much more able to absorb things with your pacing/articulation of the ideas.