Lizhand's favorite SK MAPA, HIGHER ALGEBRA ( Abstract and liner). Exercise 8, page 86. Problem 1. i) ( Z ,○) , Where a○b= a+b+1, a,b ∈ Z. Sol- i) The binary composition is closed. ii) a○(b○c)=(a○b)○c It is associative. iii) identity element e=-1 iv) a'=( -2-a) Therefore the algebraic system is a group.
How do we know that the mathematics and number system we use are correct ? That's why we always try to understand different approch Here binary operation comes into the picture so yes we can generalise this
in general, "a * a = a^2" is not always true in group theory; it only holds true for the specific case where the group operation is written as multiplication and the element "a" is being squared (i.e., multiplied by itself) with the standard notation for exponentiation used in algebra. But we can denote , a * a = a+ a+1 , At first you are showing that a*a= a^2 that means *=× and later a*a= a+a+1 this two conditions are not possible in same case , just thik , Only 3*3= 7 possible. Not 3^2= 7.
Puro vdo ta dekhe then Comment kora uchit always , ami specifically onekbar bolechi je a*a= a^2 is just a notation..binary operation multiplication hole tokhn ota actually a^2 hoye jay
@ayanchakrabortyclasses but a*a=a^2 r a*a= a+a+1 aii 2 to condition amra aksathe tou dakhate pari nah generally, only special kichu condition a 2 to case aksathe aste pare.
আমি একজন প্রাইভেট শিক্ষক। দশম শ্রেনি পর্যন্ত গনিত,ভৌতবিজ্ঞান,জীবনবিজ্ঞান এবং ইংরেজি পড়ায়। আপনার ভিডিও দেখি আমি রেগুলার। গনিতের প্রতি ভালোবাসা বেড়ে গেল আরো।
TH-cam e onekrokom mojar jinis dekhechi, jemon 4 color theorem, golden ratio. Kintu eita kothao dekhini. Eta besh valo chilo. Ekta request roilo Golden Ratio niye ekta video deben please. Kichu kichu prosno ache golden ratio niye jar answer kono video te paini.
Dada apni shudhu parben eei rokhom kore Mathematics ke interesting 🎉korte
@@abdurraqib1345 thanks❤️❤️
Lizhand's favorite SK MAPA, HIGHER ALGEBRA ( Abstract and liner).
Exercise 8, page 86.
Problem 1.
i) ( Z ,○) , Where a○b= a+b+1, a,b ∈ Z.
Sol-
i) The binary composition is closed.
ii) a○(b○c)=(a○b)○c
It is associative.
iii) identity element e=-1
iv) a'=( -2-a)
Therefore the algebraic system is a group.
@@rahuldevmandal7778 verry good
It is applicable only for a specific case we can't generalise this..
No it's generalisable
How do we know that the mathematics and number system we use are correct ?
That's why we always try to understand different approch
Here binary operation comes into the picture so yes we can generalise this
@@kanadsaha3447 mapa er integral power of an element ta pore aso ek2
vebechilam staircase paradox explain korbe 😃
@@kanadsaha3447 obosyoi korbo
in general, "a * a = a^2" is not always true in group theory; it only holds true for the specific case where the group operation is written as multiplication and the element "a" is being squared (i.e., multiplied by itself) with the standard notation for exponentiation used in algebra. But we can denote ,
a * a = a+ a+1 ,
At first you are showing that a*a= a^2 that means *=× and later a*a= a+a+1 this two conditions are not possible in same case , just thik ,
Only 3*3= 7 possible. Not 3^2= 7.
Puro vdo ta dekhe then Comment kora uchit always , ami specifically onekbar bolechi je a*a= a^2 is just a notation..binary operation multiplication hole tokhn ota actually a^2 hoye jay
@ayanchakrabortyclasses but a*a=a^2 r a*a= a+a+1 aii 2 to condition amra aksathe tou dakhate pari nah generally, only special kichu condition a 2 to case aksathe aste pare.
Ke boleche parbo na r kanoi ba parbo na
Kono special case noy ota ota just akta notation ota actually a2 noy..mapa ta dakho ek2 integral power of an element e bola ache
@@ayanchakrabortyclasses okay, ami dekhchi , but aktu obak laglo amar tai comment korlam.
Just Awesome, you are making Mathematics more Interesting.
Thanks . Keep supporting us
Legends favourite Group theory💥
Exactly❤
Yup. 🙌
Darun!!! Khub interesting laglo ❤
Thanks❤
Soboi ঠিক আছে,
আমারা যদি a*b= a+b+k , k is an integer defined kori than ,according to you , 3^2=3*3 assumes every integer..!
@@darpan6882 yes exactly
@ayanchakrabortyclasses
Interesting 😁
Tahole a^2 can be any value jeta ami ki relation define korbo binary operator ke tar i upor depend korbe..
Yes akdm
Dada class 12 r hs r jnno ekta suggestion ba important scoring maths gul .bolo...plz
Chesta korbo obosyoi
Mathematics ❌
Thala For a Reason ✅
@@Premananda_Rudra ❤️❤️❤️
Wow,darun jinis sikhlam...😮😮😮 5:02
❤❤❤
Sir group theory er course paoa jabe??
Yes paoa jabe
@@SubhadipShee-m4h 7278854833 te call kore purchase kore nao
Wonderful content! Thanks for sharing 😊 A Great mathematician.... really wonderful 👍 thanks a lot ...
❤️❤️❤️❤️
আমি একজন প্রাইভেট শিক্ষক। দশম শ্রেনি পর্যন্ত গনিত,ভৌতবিজ্ঞান,জীবনবিজ্ঞান এবং ইংরেজি পড়ায়। আপনার ভিডিও দেখি আমি রেগুলার। গনিতের প্রতি ভালোবাসা বেড়ে গেল আরো।
@@middyasamim5958 thanks a lot keep supporting us
Darun laglo sir.
❤❤❤
Erkm aro mojadar jinis chai besi besi kore jante chai aro ❤
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Wow dada , khub ❤❤
Thanks❤
Three cheers for GROUP THEORY
HIP HIP HURRAY ❤
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Eta kintu valo 😁😁
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Baap re....aladai duniyay niye chole gele ayan da...
@@csebangla3618 ❤️❤️
Group theory zindabad...❤️🙏🏻
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Ami amar class 5 er student ke dekhiyechi ora barite giye oder ma baba ke boleche eta
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bhul korecho dada . kono function thakle square hoy kibhabe? + jodi function thake tahole to square asbe na ekhane ektu goja mil ache
Achcha achcha sk mapa integral power of an element ta ek2 pore nao
@@ayanchakrabortyclasses Tumi tomar qualification ta ektu bolo to
Valo chilo😊❤👍🙏
❤❤
a*b=a+b+1 holo kno?
Ota akta relation jeta ami define korechi
TH-cam e onekrokom mojar jinis dekhechi, jemon 4 color theorem, golden ratio. Kintu eita kothao dekhini. Eta besh valo chilo.
Ekta request roilo Golden Ratio niye ekta video deben please. Kichu kichu prosno ache golden ratio niye jar answer kono video te paini.
@@PurnimaPaul-o6y obosyoi debo
Hello
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Obak korar kando 😮
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Op
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