Introduction to Set Theory

[@Iiid2]

I came here because I'm in an italian school and I don't speak italian. I go to an all math/science school and this has more info on sets than all three of my math books! Very helpful! keep it up!

[@Alex-bc3tt]

Straight forward and easy to understand. Keep up the good work

[@brandonvallejo3492]

short and sweet. You explain it better than my teacher

[@happyman]

On 6:01, some infinite sets are actually countable.

[@MyJuicehole]

Eh, countable by the formal definition of denumerability. It is still technically infinite, but instead of putting infinity it is typically just denoted as aleph (first letter of the Hebrew alphabet). And, because of this, any two sets are considered equinumerous as long as there is some bijection from one set to the other. So, say you want to compare the set of all integers to the set of all even integers. Intuition is of little help because it would seem the set of all even integers would contain half the elements of the set of all integers. However, because there exists some bijection (namely, take the transformation f(n) = 2n) from Z to the set of all even integers, these two sets are equinumerous. In fact, with infinite sets, there is something called the continuum hypothesis which says that the cardinality can only exist as one of two values: it can either be Aleph, or, the value C, which we will define as the cardinality of the set of ALL real numbers (you can look at the proof, but the set of all real numbers is uncountable). It was proven that assuming the continuum hypothesis to be correct brings up NO contradictions in set theory ... but it was also proven that assuming it false ALSO brings up no contradictions, so... there's that.

[@happyman]

Rellek to be "countable," also denumerable, the way it is used in mathematics, is to have the same cardinality as the set of counting numbers. the integers, even numbers, perfect squares, prime numbers, finite product of any countable sets etc. all have the same cardinality as counting numbers. and all of these sets are countable.

[@winterrain1947]

Get off my math level! Go back to the upper floors where u belong and quit picking on us little kids! btw this is a joke

[@DJSouthFlorida]

This video is way more descriptive compared to the video my professor had me watch. Good Job!

[@Seedofwinter]

Terrific. Textbooks, and classes in general, have a nasty habit of throwing around notation and concepts they don't explain. I thank you for your video.

[@ab-stak4657]

all I needed to know and more in just few minutes ! Brilliant!!

[@brendarojas5613]

Yep

[@dark666raver]

thank you!!!! some of us are doing distance education (e.g. at UNISA) and this was very helpful

[@fothpima]

At 6:34 you state that the cardinality of an infinite set is uncountable. You may want to add a comment here that infinite sets can be both countable and uncountable and that the cardinality is described by the cardinal numbers. Thanks for posting these mini lessons.

[@nicolasblackburnca]

Nice video. One point though, an infinite set *can* be countable because the definition of a countable set doesn't require the set to be finite, just to be mappable in a one-to-one relationship with the set (or a subset which can be finite or infinite) of natural numbers (which is itself infinite).

People like you are heroes, thankyou

[@tlmcqu80]

nice video... I'm a new computer science graduate student with a business background... I found this vid very informative as I'm attempting to increase my math skills and move over to the computer science side as it relates to programming and development... I've gotten some feedback as to what type of math computer scientist are skilled in and Discrete math is one.. the first chap in Schaum's discrete math is Set theory... keep up the good work!!! and thanks...

[@hildareels7162]

The World is a better place because they are as well as we are in it for the betterment of .ankind everywhere. Peace and prosperity to all.

[@LilHaseProductions]

2:01 what did he say?

[@hyqhyp]

This is a good video that I have used to introduce set theory to my son. However, I cringed at the error at 6:01, regarding infinite sets being uncountable. Countability leads to some of the most significant results of set theory, it is quite a shame to mis-introduce it like this. At least put some annotation on to of the video if you can to correct the definition.

[@bimalka98]

If S and T are non empty ,bounded,sub-sets of real numbers, what does the relationship S is smaller than T means? would you mind providing an answer for this?

[@kalpanasingh6833]

Good video on Set theory ( Mathematics).

[@joybray2700]

Thank YOU!!! This video was very helpful.

[@kentsanaisala7470]

This really help me a lot today

[@RGDCaliber]

Well presented, clear, informative, keep it up

[@abdulraufsaharudin9859]

wow, that was really helpful. Thanks James!

[@Mathispower4u]

Thank you!

[@arunmondal1222]

Thanks for such a good lesson for understanding set theory

[@CBaggers]

Very clear. Thankyou, please keep up the great work!

[@MrHeinnie]

Could you make videos for the relative compliment of set? Thank you.

[@reconuhd4193]

I set out as a 8th grade student to understand set theory, this video made it sounds easy, but if i read the books again, i still dont understand anything.

[@Mathispower4u]

Maybe try watching the entire playlist on set theory under the Liberal Arts Math on my site: mathispower4u.com

[@reconuhd4193]

thx

[@Abbas-Syed-Sb]

This was quite helpful. Thank you!

[@cheesetoochalk]

Thank you sir. Gotta love youtube.

[@debendra1583]

i have a doubt due to difference in answer in two books so please solve my problem sir IS THIS THE FOLOWING ARE SETS GIVE REASON FOR YOUR ANSWER (a) {1,@,ram,china} (b) { ( ) ,ram ,@, 19} ( c ) {ram ,c[0,1] ,algebra}

[@Dr.SariHamoud]

good job bro

[@rosendacaluyo362]

I hope you can make . quizzes based on your discussion sir😁

[@vanshu4320]

It is very helpful for me that you so much

[@omargigyani]

Thank you. I found it very helpful. :)

[@brendarojas5613]

3:07 *than

[@ritwikjaiswal4593]

Thanks a lot .. It was very helpful :)

[@hildareels7162]

Love those Williams Sisters. They are Top Notch. Aman Amen Amen

[@ahmadsolehin93]

at cardinality n cardinal number i dont understand... can u explain more clearly.. because im so dumb

[@kznkzndoe4538]

That's for such a good lesson !

[@VdubOndUbZ]

Thank You this was great :O)

[@Zombie81212]

i agree with the rest of the positive comments in this comment section

[@JuJuzNation]

omg thank you soooo much

[@Mathispower4u]

I have a lot more set videos in my liberal arts math video library on my site mathispower4u

[@prince8896]

VERY HELPFUL

[@tlmcqu80]

I'm sorry. I can't answer that question yet. still getting chapter one, set theory; and I have two projects I'm currently working on. I'm not in that deep yet.

[@debendra1583]

here @ is the null set or phi

[@jaimepaullamb]

many thanks!

[@MeganAglaua]

thank you so much!

[@Applepievava]

very helpful

[@glennd.merabemraltheagwen4934]

thank you

[@devdattaanjankar2669]

nice one

[@Mathispower4u]

Thank you for the comment.

[@erikdunn5137]

thanks

[@Amidejeune]

nice video

[@Matias-yp4xx]

you is very inteliyen

[@Dhaliwalhemantsingh]

thanks sir

[@brianlaudrupchannel]

im doing this on my computer course. I don't see the point.

[@charlesamofordjuoh9940]

deadass I don't understand how discrete math helps me in programming

[@brianlaudrupchannel]

Charles Amofordjuoh it dosent

[@christophersedlak1147]

thanks!!!!!!!!!

[@IvySivy]

awesome

[@jeweljoshi]

1K ❤️

[@itsme_imabanana4758]

I like algebra more than this one =_=

[@JedOpeningThings]

This is too messy for me ;(

[@The_Zenauh]

Being honest, you explain good, but with no offense, the video is boring, sorry

[@Alex-bc3tt]

Straight forward and easy to understand. Keep up the good work

[@dr.ajaikumartiwari9842]

nice one