Introduction to Set Theory

  Рет қаралды 314,930

Mathispower4u

Mathispower4u

Күн бұрын

Пікірлер: 73
@Iiid2
@Iiid2 12 жыл бұрын
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
@Alex-bc3tt 11 жыл бұрын
Straight forward and easy to understand. Keep up the good work
@brandonvallejo3492
@brandonvallejo3492 4 жыл бұрын
short and sweet. You explain it better than my teacher
@happyman
@happyman 10 жыл бұрын
On 6:01, some infinite sets are actually countable.
@MyJuicehole
@MyJuicehole 10 жыл бұрын
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
@happyman 10 жыл бұрын
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
@winterrain1947 4 жыл бұрын
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
@DJSouthFlorida 11 жыл бұрын
This video is way more descriptive compared to the video my professor had me watch. Good Job!
@Seedofwinter
@Seedofwinter 12 жыл бұрын
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
@ab-stak4657 4 жыл бұрын
all I needed to know and more in just few minutes ! Brilliant!!
@brendarojas5613
@brendarojas5613 4 жыл бұрын
Yep
@dark666raver
@dark666raver 11 жыл бұрын
thank you!!!! some of us are doing distance education (e.g. at UNISA) and this was very helpful
@fothpima
@fothpima 13 жыл бұрын
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
@nicolasblackburnca 11 жыл бұрын
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).
11 жыл бұрын
People like you are heroes, thankyou
@tlmcqu80
@tlmcqu80 12 жыл бұрын
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
@hildareels7162 6 жыл бұрын
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
@LilHaseProductions 7 жыл бұрын
2:01 what did he say?
@hyqhyp
@hyqhyp 9 жыл бұрын
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
@bimalka98 6 жыл бұрын
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
@kalpanasingh6833 6 жыл бұрын
Good video on Set theory ( Mathematics).
@joybray2700
@joybray2700 4 жыл бұрын
Thank YOU!!! This video was very helpful.
@kentsanaisala7470
@kentsanaisala7470 4 жыл бұрын
This really help me a lot today
@RGDCaliber
@RGDCaliber 12 жыл бұрын
Well presented, clear, informative, keep it up
@abdulraufsaharudin9859
@abdulraufsaharudin9859 10 жыл бұрын
wow, that was really helpful. Thanks James!
@Mathispower4u
@Mathispower4u 10 жыл бұрын
Thank you!
@arunmondal1222
@arunmondal1222 9 жыл бұрын
Thanks for such a good lesson for understanding set theory
@CBaggers
@CBaggers 12 жыл бұрын
Very clear. Thankyou, please keep up the great work!
@MrHeinnie
@MrHeinnie 13 жыл бұрын
Could you make videos for the relative compliment of set? Thank you.
@reconuhd4193
@reconuhd4193 10 жыл бұрын
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
@Mathispower4u 10 жыл бұрын
Maybe try watching the entire playlist on set theory under the Liberal Arts Math on my site: mathispower4u.com
@reconuhd4193
@reconuhd4193 10 жыл бұрын
thx
@Abbas-Syed-Sb
@Abbas-Syed-Sb 11 жыл бұрын
This was quite helpful. Thank you!
@cheesetoochalk
@cheesetoochalk 11 жыл бұрын
Thank you sir. Gotta love youtube.
@debendra1583
@debendra1583 11 жыл бұрын
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
@Dr.SariHamoud 9 жыл бұрын
good job bro
@rosendacaluyo362
@rosendacaluyo362 3 жыл бұрын
I hope you can make . quizzes based on your discussion sir😁
@vanshu4320
@vanshu4320 4 жыл бұрын
It is very helpful for me that you so much
@omargigyani
@omargigyani 13 жыл бұрын
Thank you. I found it very helpful. :)
@brendarojas5613
@brendarojas5613 4 жыл бұрын
3:07 *than
@ritwikjaiswal4593
@ritwikjaiswal4593 10 жыл бұрын
Thanks a lot .. It was very helpful :)
@hildareels7162
@hildareels7162 6 жыл бұрын
Love those Williams Sisters. They are Top Notch. Aman Amen Amen
@ahmadsolehin93
@ahmadsolehin93 12 жыл бұрын
at cardinality n cardinal number i dont understand... can u explain more clearly.. because im so dumb
@kznkzndoe4538
@kznkzndoe4538 10 жыл бұрын
That's for such a good lesson !
@VdubOndUbZ
@VdubOndUbZ 13 жыл бұрын
Thank You this was great :O)
@Zombie81212
@Zombie81212 4 жыл бұрын
i agree with the rest of the positive comments in this comment section
@JuJuzNation
@JuJuzNation 11 жыл бұрын
omg thank you soooo much
@Mathispower4u
@Mathispower4u 11 жыл бұрын
I have a lot more set videos in my liberal arts math video library on my site mathispower4u
@prince8896
@prince8896 12 жыл бұрын
VERY HELPFUL
@tlmcqu80
@tlmcqu80 12 жыл бұрын
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
@debendra1583 11 жыл бұрын
here @ is the null set or phi
@jaimepaullamb
@jaimepaullamb 11 жыл бұрын
many thanks!
@MeganAglaua
@MeganAglaua 10 жыл бұрын
thank you so much!
@Applepievava
@Applepievava 12 жыл бұрын
very helpful
@glennd.merabemraltheagwen4934
@glennd.merabemraltheagwen4934 11 жыл бұрын
thank you
@devdattaanjankar2669
@devdattaanjankar2669 10 жыл бұрын
nice one
@Mathispower4u
@Mathispower4u 10 жыл бұрын
Thank you for the comment.
@erikdunn5137
@erikdunn5137 11 жыл бұрын
thanks
@Amidejeune
@Amidejeune 13 жыл бұрын
nice video
@Matias-yp4xx
@Matias-yp4xx 9 жыл бұрын
you is very inteliyen
@Dhaliwalhemantsingh
@Dhaliwalhemantsingh 11 жыл бұрын
thanks sir
@brianlaudrupchannel
@brianlaudrupchannel 11 жыл бұрын
im doing this on my computer course. I don't see the point.
@charlesamofordjuoh9940
@charlesamofordjuoh9940 10 жыл бұрын
deadass I don't understand how discrete math helps me in programming
@brianlaudrupchannel
@brianlaudrupchannel 10 жыл бұрын
Charles Amofordjuoh it dosent
@christophersedlak1147
@christophersedlak1147 3 жыл бұрын
thanks!!!!!!!!!
@IvySivy
@IvySivy 11 жыл бұрын
awesome
@jeweljoshi
@jeweljoshi 2 жыл бұрын
1K ❤️
@itsme_imabanana4758
@itsme_imabanana4758 5 жыл бұрын
I like algebra more than this one =_=
@JedOpeningThings
@JedOpeningThings 12 жыл бұрын
This is too messy for me ;(
@The_Zenauh
@The_Zenauh 3 жыл бұрын
Being honest, you explain good, but with no offense, the video is boring, sorry
@Alex-bc3tt
@Alex-bc3tt 11 жыл бұрын
Straight forward and easy to understand. Keep up the good work
@dr.ajaikumartiwari9842
@dr.ajaikumartiwari9842 9 жыл бұрын
nice one
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