Group and Abelian Group
ฝัง
- เผยแพร่เมื่อ 10 ก.ย. 2024
- Network Security: Group and Abelian Group
Topics discussed:
1) The definition of group and abelian group.
2) Properties to be satisfied for the set of elements to be a group and abelian group.
3) Explanation on closure, associative, identity, inverse, and commutative properties.
4) Solved problem of determining (Z, +) a group and abelian group.
5) Various mathematical notations for a set of numbers in number theory.
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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.
-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, +).
@@tesfayeyisahak
@@tesfayeyisahak the set used in the HW ques is Z* and not Z+ .
Beautifully explained with such a direct approach. Loved it.
Beautiful explanation ...In Closure property ,5-2=3
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.
then teach us vector spaces too @nishith sir please :)
@@shakirashaikh Now, you've seen the same video and hence you can understand vector spaces yourself ma'am.
For the 1st time I understood this topic very well
Very clearly explained, thanks so much!
Really smooth explanation. Understood with just one watch. 🥇🏆🏅
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
At 6:14, 5-2 must be +3
Yes you are right it should be +3
damn, too good presentation & explanation man, please keep up the good work.
very well explained. thank you for all the help.
and i want more videos from you with fields odered fields because those are the concepts i am stuck with
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
That was helpful...do one for binary operations
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 ?
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
@@Anonyymous818 Careful, that Z* is all integets but 0. Doesn't satisfy.
yup it's not a group but a semi group cuz it satisfies closure and associative property.
Excellently explained ❤️
THANK YOU SIR❤
❤❤❤ your explanation is excellent
Sir in closure property a=5 ,b=-2 then it is 3 not -3 sir...
very clear and useful!! many thanks; ❤️
Sir, 5+(-2) = 3 ...
thank you so much it was an amazing explanation
thank you or this lovely explanation
Very good explanation
Nice explanation sir
i love this. Thank you so much
Wonderful explanation 😊
Love you very clear uni explanation terrible yours good
homework question , initially , + is not binary operation on Z*
Excellent sir very useful
Thanks a lot 🎉
Thank you so much sir!!!☺️
Thank u so so much sir ♥️♥️♥️♥️
6:09 it should be 3 not -3. But it is good and comprehensible presentation 👏👏
it was just excellent
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 !
(z*,+) is not a group because no 0 exists, eliminating the identity criteria.
Thanks sir
Thanku sir
Sir the result of associative and commutave must be their in group or just need to get RHS=LHS
we need to get just RHS=LHS
Thanku a lot sir
Thankyou ❤️
Thank u....
(Z*, +) is not a group as it does not satisfy inverse.
Sir...N is not a group under addition and multiplication ...is it correct
Hi
Z+ means positive integers know bro
I hope
Yes
😊
Thankyou
(Z*,+) is not a group
It's a ring
Yes because inverse element is not exist in z+
@@A-ONE991doesn't*
@@omkar6649😂
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.
O thank you!
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
Do you know the answer
Please put videos for subgroup and normal subgroup
(Z* +) is not a group sir
How
@@CodingWithMR i believe it failed the inverse and identity element
@@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.
@@xinpingdonohoe3978 how 0 is not in Z
@@comradenikolatesla1998
The set Z* is defined as Z\{0}
i feel like teacher is not same as in c programming and preposition logic
Sir always we take identity element is zero
verryyyy nice
how is 5+(-2)=-3??? {at 6:02}
No, it is not a group since closure property not satisfied
❤❤❤
Where did 5 in closure came from??
time?
it is not a group since there is no identity element which is zero in that set
calculation for closure is wrong not -5
Eduphile??
💥💥💥💥💥💥💥💥💥💥
Sorry lads but I haven’t got the patience!
Y’all gotta find someone else
is it me or does he sound like chris griffin ?
"L."
Gulo n'yo naman. Edi hindi group yan?
No inverse property unsatisfied.
Excellent explained
❤❤❤
(Z+,+) is not a group