The author clearly has a skill of providing clear explanations! Well done, sir!
@WrathofMath
7 ай бұрын
Many thanks!
@KermitTheHermit.
Жыл бұрын
Understood perfectly! Thank you for a different perspective. Was stuck with the textbook definition for long. Thanks again🙏🏻😊
@WrathofMath
Жыл бұрын
Glad to help, thanks for watching!
@wenzhang365
2 ай бұрын
Please keep up the good work, thank you!
@VijitChandna
Жыл бұрын
First! Tommorow is my exam and I had commented on his channel about this topic and he sent me an unlisted link! Thank you so much :)
@lamyamalcolm-uu8zp
5 ай бұрын
Very skillful and talented, thank you so much. You videos help me a lot with my studies here.
@WrathofMath
5 ай бұрын
Glad to hear it, thanks for watching!
@claytonbenignus4688
7 ай бұрын
I Get It!!! You could say that if you take a Zane Grey Novel and transform a few words (Rancher's Daughter = Martian Princess; Rifle = Disintegrator; Stage Coach = Rocket Shoip; The Cavalry = Star Fleet; etc.), you get a Star Trek Episode . . .
@gabriels.i.780
11 ай бұрын
Thank you so much! Very clear and rich explanation. I would like to ask...Isomorphism seems pretty restrictive as a way to study identity/similarity between groups. Is there any concept in abstract algebra that can account for "weaker" forms of similarity? Thanks!
@WrathofMath
11 ай бұрын
Great question and the answer is a big yes! kzitem.info/news/bejne/04Cm22Zoo3-WfI4&pp=ygUSaG9tb21vcnBoaWMgZ3JvdXBz
@MrCoreyTexas
2 ай бұрын
For anyone interested, you should look up the Wikipedia on the Klein Group with 4 elements
@JTan-fq6vy
Ай бұрын
Thanks for the great video! Is there any theory that deals with the generalization of this isomorphism? For example, if I want to verify an equivalent relation between two mathematical objects with arbitrary properties (not specifically the ones of binary operator for groups), is there a modification of the definition in time 1:50 that can give a generalized notion of isomorphism?
@alexdrougkas208
Жыл бұрын
Thank you so much for the lecture. Keep up the great quality of work!
@WrathofMath
Жыл бұрын
Thank you Alex!
@jaaaaaaaaaaaac6986
7 ай бұрын
very nice video!you should put this into your list, can't find this one in the list.
@WrathofMath
7 ай бұрын
In the playlist? Weird, I see it. It is right after Permutation groups and before Order of Elements in a Group! I have spreadsheets on spreadsheets to keep all my playlists organized haha!
@kabirbhattacharyya9014
Ай бұрын
One thing I was wondering.... How does isomorphism "transforms" a group to another? Like how I thought.... It's like a bridge to Each storeys of two almost identical buildings. One is red, one is blue.. etc. what exactly I'm calling the "Isomorphism"? Also could you help me with the "transforms" a group to another?
@ahasdasetodu6304
10 ай бұрын
The second theorem mentions a set of all groups but from my understanding of set theory such a thing would lead to contradictions the same way a set of all sets does. Wouldn't it be better to say a class of all groups?
@madomalene5898
8 ай бұрын
For the first example,how did you obtain the second table. What rules were you using to perform the multiplication
@lemonandgaming6013
6 ай бұрын
he just renamed all elements and the operation of g1. that is how he got g2. then he proved that these groups are isomorphic (the same), which is trivial since one is a renaming of the other
@gp2111
7 ай бұрын
For the portion where you discuss ways to find groups that are NOT isomorphic, you give 4 criteria but I'm curious what the difference between #2 and #3 are? If a G1 has an element of order n, does that not make it cyclic, which would be the same as #2?
@WrathofMath
7 ай бұрын
Thanks for watching and for the question! Perhaps you're confused because you think I mean 'n' to be the order of the group? I simply mean n to be a finite number, and a group having an element of finite order does not force it to be cyclic. Does that answer your question?
@gp2111
7 ай бұрын
@@WrathofMath Gotcha! It does answer my question. Thanks.
@2kreskimatmy
8 ай бұрын
do you get into Cayley's theorem in some video?
@VijitChandna
Жыл бұрын
The chapters seem to say homomorphism for some reason
@WrathofMath
Жыл бұрын
Looks like they're correct in the description, will probably just take some time to update hopefully!
@algierithm4443
6 ай бұрын
Hello what notepad are you using? Thanks
@WrathofMath
6 ай бұрын
Notability!
@algierithm4443
5 ай бұрын
@@WrathofMath thanks much. btw, I love your videos.
@scito1541
Жыл бұрын
so isomorphism is a homomorphism that is a bijection right?
@scito1541
Жыл бұрын
if anyone wants to know i asked Bing AI and it basically said yes
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