Group and Abelian Group

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  • Опубліковано 25 січ 2025

КОМЕНТАРІ • 107

  • @123arskas
    @123arskas 2 роки тому +30

    Beautifully explained with such a direct approach. Loved it.

  • @bilaljan321
    @bilaljan321 2 роки тому +75

    Home work question given at 10:13 is not a group as 3 + (-3) = 0 and 0 is not the Z'. So its not closed with addition operation.

    • @tesfayeyisahak
      @tesfayeyisahak Рік тому +6

      -3 first of all is not in the set of z+, of course it satisfies closurity property, but the reason that it is not a group is because It does'nt have an identity element and inverse just as (N, +).

    • @deletedfrom1988
      @deletedfrom1988 11 місяців тому

      @@tesfayeyisahak

    • @18fatima15
      @18fatima15 9 місяців тому +9

      @@tesfayeyisahak the set used in the HW ques is Z* and not Z+ .

  • @NishithSavla
    @NishithSavla 2 роки тому +14

    Thanks a lot for this explanation. It was all going over my head while learning vector space. Now I'll be able to understand it all.

    • @shakirashaikh
      @shakirashaikh 2 роки тому +1

      then teach us vector spaces too @nishith sir please :)

    • @NishithSavla
      @NishithSavla 2 роки тому

      ​@@shakirashaikh Now, you've seen the same video and hence you can understand vector spaces yourself ma'am.

  • @luckieboy_logee
    @luckieboy_logee 2 роки тому +28

    Beautiful explanation ...In Closure property ,5-2=3

  • @Sammie554
    @Sammie554 3 місяці тому +2

    Thankyouu so much sir for that cain short cut ❤ the whole video is amazing

  • @photolab6712
    @photolab6712 6 місяців тому +2

    For the 1st time I understood this topic very well

  • @ocular4755
    @ocular4755 3 місяці тому +3

    insanely good explanation

  • @erolakkas6410
    @erolakkas6410 Рік тому +1

    Really smooth explanation. Understood with just one watch. 🥇🏆🏅

  • @valeriereid2337
    @valeriereid2337 3 місяці тому +1

    You did a fantastic job with this topic. Thank you.

  • @williesanape3900
    @williesanape3900 2 роки тому +7

    Very clearly explained, thanks so much!

  • @Chuyaxz
    @Chuyaxz Рік тому +2

    6:09 it should be 3 not -3. But it is good and comprehensible presentation 👏👏

  • @MdHumayun-pm2kp
    @MdHumayun-pm2kp 3 роки тому +24

    At 6:14, 5-2 must be +3

    • @asadahmed597
      @asadahmed597 2 роки тому +2

      Yes you are right it should be +3

  • @shubhratbro7362
    @shubhratbro7362 2 роки тому +2

    Excellently explained ❤️

  • @donthusravya2026
    @donthusravya2026 3 роки тому +5

    Sir your videos are really intelligible and I liked them very much .Could u please upload the videos in a faster rate? I am so eager to learn the whole subject

  • @shikha7873
    @shikha7873 Рік тому

    ❤❤❤ your explanation is excellent

  • @simpleandminimalmaybe
    @simpleandminimalmaybe Рік тому +1

    very well explained. thank you for all the help.

  • @nightmare399
    @nightmare399 8 місяців тому

    and i want more videos from you with fields odered fields because those are the concepts i am stuck with

  • @denishnatiuk921
    @denishnatiuk921 2 місяці тому

    very intuitive explaination

  • @AlessandroZir
    @AlessandroZir 2 роки тому +1

    very clear and useful!! many thanks; ❤️

  • @mahadihassanriyadh
    @mahadihassanriyadh 5 місяців тому

    damn, too good presentation & explanation man, please keep up the good work.

  • @ramashukla541
    @ramashukla541 Рік тому

    Wonderful explanation 😊

  • @Sravani-n9r
    @Sravani-n9r 11 місяців тому

    Nice explanation sir

  • @himanshitangariya1275
    @himanshitangariya1275 Рік тому +1

    THANK YOU SIR❤

  • @apsarakarunarathna9668
    @apsarakarunarathna9668 2 місяці тому

    This is great... thankyou

  • @DumolwenkosiVhumbunu
    @DumolwenkosiVhumbunu 8 місяців тому

    That was helpful...do one for binary operations

  • @adhityaadhi9107
    @adhityaadhi9107 Рік тому +1

    Sir in closure property a=5 ,b=-2 then it is 3 not -3 sir...

  • @HakizimfuraInnocent
    @HakizimfuraInnocent Місяць тому

    Wawooo this explaination is crealy

  • @farmygaming9609
    @farmygaming9609 Рік тому +1

    homework question , initially , + is not binary operation on Z*

  • @MohaMohamoud-r2d
    @MohaMohamoud-r2d Рік тому

    thank you so much it was an amazing explanation

  • @aayrakumari7816
    @aayrakumari7816 2 роки тому

    Thank u so so much sir ♥️♥️♥️♥️

  • @sarithachavatapalli1560
    @sarithachavatapalli1560 2 роки тому

    Excellent sir very useful

  • @mohamedaminenadiri2853
    @mohamedaminenadiri2853 Рік тому

    thank you or this lovely explanation

  • @ExploringWorld100
    @ExploringWorld100 2 роки тому

    Excellent explained

  • @adithibhat7277
    @adithibhat7277 Рік тому

    i love this. Thank you so much

  • @aswanthajay3034
    @aswanthajay3034 2 роки тому +5

    Sir, 5+(-2) = 3 ...

  • @nehachhetri7115
    @nehachhetri7115 3 роки тому

    Thank you so much sir!!!☺️

  • @aakashjason803
    @aakashjason803 Рік тому +2

    Hw answer
    Z+ --> set of positive integers
    Identity -->0 ( identity elmt in addition)
    Consider inverse property..
    Since z+ consists of all positive integers, obviously sum of any two elements won't give identity elmt 0. So each element in z+ does not have a corresponding inverse ---> violation of CAIN ---> hence { Z+ , +} not a group

  • @EdrisKhan-w1u
    @EdrisKhan-w1u Рік тому

    Thanks a lot 🎉

  • @saeedsharif2463
    @saeedsharif2463 2 роки тому +1

    Sir the result of associative and commutave must be their in group or just need to get RHS=LHS

  • @nightmare399
    @nightmare399 8 місяців тому

    yeah bro thanks according to me the question you gave at last is z(binary operation), +) is it a group
    soln (according to me i think it is right)
    CAIN - closure - yes a,b (belongs to )P a*b (belongs to )P yes
    associative subtraction is not associative so i stopped here it self so it is not an group that's all !

  • @genjishimada3767
    @genjishimada3767 Рік тому

    Love you very clear uni explanation terrible yours good

  • @kvenkataraju
    @kvenkataraju Рік тому +1

    (Z*, +) is not a group as it does not satisfy inverse.

  • @anishaa3557
    @anishaa3557 2 роки тому

    Sir...N is not a group under addition and multiplication ...is it correct

  • @arnavsrivastava7763
    @arnavsrivastava7763 2 роки тому

    how is 5+(-2)=-3??? {at 6:02}

  • @rajeshprajapati4863
    @rajeshprajapati4863 2 роки тому +33

    Answer to H.W :
    Z* = {... -3, -2, -1, 1, 2, 3 ...} under Addition.
    Closure => Any Two Numbers : -1, 1 ∈ Z* but -1 + 1 = 0 ∉ Z*
    Since, one of the property out of CAIN is not satisfied. Hence, (Z*, +) is not Group. Right ?

    • @Anonyymous818
      @Anonyymous818 Рік тому +2

      Z is denoted as an integer and an integer is a set of positive and negative numbers including 0 hence Z,+ is satisfied and it is an abelian group

    • @koolkoolkoopa
      @koolkoolkoopa Рік тому +2

      @@Anonyymous818 Careful, that Z* is all integets but 0. Doesn't satisfy.

    • @VikashYadav0067
      @VikashYadav0067 Рік тому +1

      yup it's not a group but a semi group cuz it satisfies closure and associative property.

  • @gursheenkaur9586
    @gursheenkaur9586 2 роки тому +2

    i feel like teacher is not same as in c programming and preposition logic

  • @stacydevries4241
    @stacydevries4241 Рік тому +1

    (z*,+) is not a group because no 0 exists, eliminating the identity criteria.

  • @sravanthikumarapu4640
    @sravanthikumarapu4640 2 роки тому

    it was just excellent

  • @selvamathik8982
    @selvamathik8982 Рік тому

    Please put videos for subgroup and normal subgroup

  • @pittakumar2612
    @pittakumar2612 Рік тому

    Sir always we take identity element is zero

  • @VivekSingh-vs2ex
    @VivekSingh-vs2ex 2 роки тому

    Thankyou ❤️

  • @shaiksameer1890
    @shaiksameer1890 Рік тому

    Thanks sir

  • @kalpalatha4463
    @kalpalatha4463 Рік тому +1

    Hi
    Z+ means positive integers know bro
    I hope

  • @S.Vanlalchhana
    @S.Vanlalchhana 2 роки тому +1

    Sir, can you please solve this problem Prove that G is a abelian if b^{-1}a^{-1}ba=e for all a, b€G

  • @mohdazeem3260
    @mohdazeem3260 3 роки тому

    Thanku a lot sir

  • @tiny_jam7897
    @tiny_jam7897 2 роки тому

    Where did 5 in closure came from??

  • @ayesharanijahangeerkhan210
    @ayesharanijahangeerkhan210 Рік тому

    Thanku sir

  • @mihirmathur5855
    @mihirmathur5855 2 роки тому

    No, it is not a group since closure property not satisfied

  • @aayrakumari7816
    @aayrakumari7816 2 роки тому

    Thank u....

  • @ankitsajwan6685
    @ankitsajwan6685 2 роки тому

    Thankyou

  • @asjedits2311
    @asjedits2311 2 роки тому +24

    (Z* +) is not a group sir

    • @NoobROHIT20
      @NoobROHIT20 2 роки тому

      How

    • @michaellee7933
      @michaellee7933 2 роки тому +1

      @@NoobROHIT20 i believe it failed the inverse and identity element

    • @xinpingdonohoe3978
      @xinpingdonohoe3978 2 роки тому +1

      @@michaellee7933 it fails all except associativity.
      a+(-a)=0, but 0 is not in the group and hence can't act as an identity, meaning that there is nowhere for an inverse to map to.
      This means it's not closed, it's got no identity and from having no identity can have no inverses.

    • @comradenikolatesla1998
      @comradenikolatesla1998 Рік тому

      @@xinpingdonohoe3978 how 0 is not in Z

    • @xinpingdonohoe3978
      @xinpingdonohoe3978 Рік тому +1

      @@comradenikolatesla1998
      The set Z* is defined as Z\{0}

  • @NFECTUS1
    @NFECTUS1 2 роки тому +59

    (Z*,+) is not a group

    • @omkar6649
      @omkar6649 Рік тому +4

      It's a ring

    • @A-ONE991
      @A-ONE991 Рік тому +9

      Yes because inverse element is not exist in z+

    • @Shoya_Ishida_69
      @Shoya_Ishida_69 Рік тому +3

      ​@@A-ONE991doesn't*

    • @gulzerhossen9608
      @gulzerhossen9608 11 місяців тому +1

      ​@@omkar6649😂

    • @rihanawab7438
      @rihanawab7438 9 місяців тому +4

      It's a group
      Because
      0 is the identity element for addition we are not talking about whether it is belongs to integers or not.
      And same as for 1.
      Yes when it comes to multiplication then it's not a group.

  • @MarionBesterMaganga
    @MarionBesterMaganga 11 місяців тому

    it is not a group since there is no identity element which is zero in that set

  • @pinkysingh6147
    @pinkysingh6147 2 роки тому

    verryyyy nice

  • @JaySE_25
    @JaySE_25 Рік тому

    O thank you!

  • @IslombekNematov-f5s
    @IslombekNematov-f5s Рік тому

    ❤❤❤

  • @harshitkumawat4987
    @harshitkumawat4987 2 роки тому

    calculation for closure is wrong not -5

  • @Hans_Magnusson
    @Hans_Magnusson Рік тому

    Sorry lads but I haven’t got the patience!
    Y’all gotta find someone else

  • @MSSSashwathanS
    @MSSSashwathanS 2 роки тому

    is it me or does he sound like chris griffin ?

  • @bennyhood9122
    @bennyhood9122 Рік тому

    Eduphile??

  • @tejask6854
    @tejask6854 2 роки тому

    💥💥💥💥💥💥💥💥💥💥

  • @tiny_jam7897
    @tiny_jam7897 2 роки тому

    Gulo n'yo naman. Edi hindi group yan?

  • @johnstfleur3987
    @johnstfleur3987 Рік тому

    "L."

  • @Sagardeep_Das
    @Sagardeep_Das Рік тому

    No inverse property unsatisfied.

  • @Rohit_Singh7091
    @Rohit_Singh7091 Рік тому

    Very good explanation

  • @amudy9657
    @amudy9657 13 днів тому

    Thanks

  • @IslombekNematov-f5s
    @IslombekNematov-f5s Рік тому

    ❤❤❤

  • @jeevajeeva-c2b
    @jeevajeeva-c2b 11 місяців тому

    (Z+,+) is not a group