Elementary Set Theory in 49 minutes

[@emmettgriner6345]

I am a 68 year old former accounting professor. Your elementary set theory video should be required viewing for accounting students, and I believe it would have value for students in just about any subject. By focusing on general purpose reasoning skills the video transcends subject matter boundaries. By spending a couple of hours with your video today and referring back to it as the need arises, students could avoid countless hours, days, and weeks of pointless flailing around in the future. Specific content comes and goes but logic is here to stay. Your video proves the old adage that there's nothing more practical than a good theory.

[@DennisDavisEdu]

Thank you Professor, you lifted my spirits for the day. I agree the topic is general and can be applied to many areas of study. Thanks for your kind words!

[@abrrrik]

i don't usually write comments, but this video is so good that i can't leave without saying that

[@Mikalinium]

This video is extremally underrated. I'm surprised that this has only 15k views for such quality.

[@trtlphnx]

As A Mathematicain, I Love Your Presentations.

[@silambarasanb2475]

Thanks for the video. It was really helpful. I like the crisp no-nonsense delivery of yours. The animations are very smooth, helping better absorption of the material delivered.

[@krishnamurari9130]

Thanks sir u are a awesome teacher. Your style of teaching is unique and I like it very much. I found this channel yesterday by KZbin's recommendations and since then I watched 27 of your videos. You are really awesome please upload more videos on other topics.

[@samburdge9948]

I think you do great work chief….one of, possibly favorite math channels….you should be way higher viewership…..hope you are using other platforms…..gods bless

[@_jamal_]

Thanks Sir ! please keep helping us, y're an excellent teacher.

[@femiadeoye4011]

I now understand ser theory Thanks to your simple explanation calm voice and what you do that helps you solve problem easily

[@educationispower4069]

Many many thanks for the video Sir ❤❤❤🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳Love from India ❤❤

[@Luke-dy7np]

I am happy to see another video by you, since you teach in a way which is very easy to understand.

[@rossduncan20]

Thank you so much. You've just made my first three weeks of my Masters make sense in 10 minutes

[@03BangBang]

This video came out one day before my 33rd birthday...May the Fourth be with You

[@DennisDavisEdu]

...and also with you!

[@danielEpifanov]

wow you are an awesome lecturer

[@sneakypress]

I love ❤ set theory . I have old (1980s) Year 8, and Year 9, maths books and I studied the set theory chapters in great detail. I took very comprehensive notes. For some reason I find it very interesting. It helped a lot with probability and statistics. I like the older mathematics textbooks. Your information and teaching methods are great. 🥳

[@sciencedotexplain3654]

Sir I am happy to seeing a new video from Bangladesh,,,,thank you sir❤️

[@ITLCstudios]

You are the best teacher❤️

[@Qongrat]

Wowuuuh - super clear and perfect explanation straight to the point. This is great.

[@abrrrik]

the best set theory explanation ever

[@returned_to_monke8872]

wow, this is gonna be really helpful. Thank you!

[@afreenislam8342]

Thankyou so much sir, We want more videos like this on another topics..

[@arslanarslan9432]

this channel is amazing. Gracias.

[@nijwmsha]

Best VDO. All in One 15:05 ❤

[@arnazaron]

A VERY good introduction. Thank you!

[@redwonsagor3901]

A true Genuis man.

[@humester]

Wow! You are the best!

[@humester]

N_0 and N_1 are used to distinguish between a set of natural numbers beginning with zero or one. This notation removes the ambiguity. (Since I can't paste in the actual figures, a_b means a-subscript-b. Also, assume the N is the one Dennis shows with double lines.)

[@DennisDavisEdu]

That is an interesting remedy Mr Fever, one I wasn't aware of. Like I said in the video, this didn't seem to be an issue when I was a student. I've also seen ℤ+ (ℤ with a super-scripted +) used to denote positive integers which would fill in for N-sub-1 as you describe. I decided not to give the issue any more time or attention in the video, but students should be aware that there is room for ambiguity. Thanks for your comment!

[@olusegunolumide4168]

Thank you soo much for the detailed explanation ❤❤😊

[@AgathaYahaya-ee3bi]

Thank you sir. I learnt a lot.

[@abdulrazaqevp]

Another level of teaching 👍🏻

[@DennisDavisEdu]

Glad you think so!

[@jasdeep4000]

This video is superb. Thank you.

[@carolinemudenda2495]

Thank you sir,I now understand sets.

[@andrej5027]

Thank you sooooo much for making this video dude!!!!!!!!!!!!

[@LetsLearnMathTogether]

Thank you Dennis Davis!

[@motivationformuslims1214]

@Dennis Davis Sir I have a question: If the empty is a subset of every set, the how is U complement equal to the empty set. ( Since the empty set is a part of U and not outside it)?

[@DennisDavisEdu]

That's a great question. The Empty set is rather strange: it is an idea more than a tangible thing we can examine. The Empty set is a subset of every set simply by definition. When we get to Power sets (the last topic covered in this video), the Empty set is included as one of the subsets of every set (including the Universal set) to provide mathematical closure an completeness to the binary pattern I show. The cardinality of a Power set is 2 raised to the power of the set's cardinality only if we include the empty set as one of the subsets. This is my engineering answer, a mathematician might have a more convincing response. Otherwise when filter conditions yields the "nothing" concept, we represent it with the Empty set. And that's why the complement of the Universal set is the Empty set: What is the answer to the question: "What objects are not in the set that contains all objects?" The answer is "nothing" and hence the Empty set. I confess there are some concepts that as an engineer, I cannot provide as rigorous an explanation as a mathematician might. I hope this does not detract significantly from your enjoyment or learning experience. Best Regards, Dennis

[@motivationformuslims1214]

@@DennisDavisEdu great reply sir. Thanks. Yes I myself think that such would have been the answer since some things in mathematics probably run just by definitions. And thankfully for us as engineers, estimations make our day.

[@anthonyleineb7228]

Really informative video. Great quality and content. Keep it up!

[@The_clinic90]

cantor did a really work

[@saumyasharma7436]

this should be viral

[@MaryAdeagbo]

Incredible 💯

[@ChinnyBlack_B]

Thank u sir. God bless u

[@d.youtubr]

Please another video with set relations and functions❤

[@alexbennie]

Aaaah! I was soo waiting for the reason why Integers = /MathBB{Z}

[@motivationformuslims1214]

Thanks. Amazing.

[@Dzambo99]

Correct me if I'm wrong, but on 38:00, shouldn't the xor of 3 sets exclude the center where they all combine as well?

[@DennisDavisEdu]

The subset consisting of the intersection of all 3 sets is included in the XOR of all three. First consider {G ⊗ F}: It consists of the "half-moon" {G not in F} unioned with the "half-moon" {F not in G}. Two Venn pieces that are not in the XOR are the intersection of G and F. This includes the middle piece. So when you add the ⊗S operation, the middle piece is included again because it's a member of S but not {G ⊗ F}. It's a little confusing but if you step through the operations one-at-a-time it makes more sense. The general rule for any number of sets (not just 3) becomes: If a fragment of a Venn diagram is the intersection of an odd number of sets, then it's a member of the XOR of all the sets. Because they'll "cancel out" two-by-two (I don't know a better way to explain it without drawing a picture) and any odd numbered element will be left to be in the XOR of all the sets.

[@AG-sp8tc]

The picture of subset at 16:10 and the picture of a proper subset on 18:27 are exactly the same. In both pictures, all elements of A are elements of B and B has at least one more element. So why is it that one is called "subset" and the other "proper subset"? This is confusing. Is there an explanation?

[@DennisDavisEdu]

A proper subset is the most common type of subset. When I introduced the topic at 16:10 I drew a normal (proper) subset. Then later I needed to distinguish between these symbols: ⊂ ⊆ ⊇ ⊃ So to explain the bar underneath the symbol I needed to show that the sets could be equal. When most people think of "subset" they are probably thinking "proper subset" without thinking it has a special name. So in general, I think subset and proper subset are almost always the same thing. Maybe it just seems strange that the common case has the special name (proper).

[@kdramalover2121]

Thank you ❤

[@navigatroncidadesinteligentes]

[@ogbonnaconfidence8902]

This video is a do helpful

[@imimran924]

Sir, make videos on algebra basic to advance, please

[@femiadeoye4011]

Nice sir

[@painpeace3619]

Good video

[@ppali11]

How is it possible that there are infinite sets differing in cardinality? If equality of cardinalities depends on existence of bijection, that is on ability of pairing all elements, then the argument for one infinite set being bigger breaks down: we will never run out of elements from one set to pair up with elements of the other. What is clear for finite sets is not so for infinite. Power set of infinite set is supposed to be bigger than the set itself but it is impossible to run out of elements in either, so the reasoning really breaks down, and the ability of pairing elements cannot be the basis of the proofs. Is there another reason to consider one infinite set as bigger that the other?

[@DennisDavisEdu]

You ask deep and interesting questions about levels of infinity suitable for discussion between mathematicians and philosophers. However, I'm just an engineer and my interest in a field extends to extracting what I need from it to solve problems. So I don't have anything insightful to share on the topic. But I agree your questions are good ones.

[@jmacfilj5466]

Ótimo!

[@a.d.w0009]

WOW !!!! Just That

[@Velereonics]

Who are you and what have you done with John Michael Godier But seriously you guys have the exact same diction. timbre, and tone.

[@rotagbhd]

{ } are BRACES, not "curly braces'

[@DennisDavisEdu]

I hope this didn't spoil the video for you.

[@aLittlePal]

never had the thought of the need to study this, so this thing is called set theory in mathematics, quite a big word for such common sense, or maybe this is the difference between people, some people needed to study this for their lack of logic and reasoning.

[@DennisDavisEdu]

I agree there's nothing puzzling about Set Theory, but it is used in so many disciplines that a uniform vocabulary and symbology is helpful. So this type of video might be considered a case of putting a name to a face that's already familiar through common sense.