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 . . .
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!
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?
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?
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?
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!
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
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?
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?
The author clearly has a skill of providing clear explanations! Well done, sir!
Many thanks!
Understood perfectly! Thank you for a different perspective. Was stuck with the textbook definition for long. Thanks again🙏🏻😊
Glad to help, thanks for watching!
Please keep up the good work, thank you!
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 :)
Very skillful and talented, thank you so much. You videos help me a lot with my studies here.
Glad to hear it, thanks for watching!
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 . . .
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!
Great question and the answer is a big yes! th-cam.com/video/rJpu22jMeIY/w-d-xo.html&pp=ygUSaG9tb21vcnBoaWMgZ3JvdXBz
Thank you so much for the lecture. Keep up the great quality of work!
Thank you Alex!
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?
For anyone interested, you should look up the Wikipedia on the Klein Group with 4 elements
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?
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?
very nice video！you should put this into your list, can't find this one in the list.
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!
do you get into Cayley's theorem in some video?
For the first example,how did you obtain the second table. What rules were you using to perform the multiplication
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
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?
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?
@@WrathofMath Gotcha! It does answer my question. Thanks.
The chapters seem to say homomorphism for some reason
Looks like they're correct in the description, will probably just take some time to update hopefully!
Hello what notepad are you using? Thanks
Notability!
@@WrathofMath thanks much. btw, I love your videos.
so isomorphism is a homomorphism that is a bijection
right?
if anyone wants to know
i asked Bing AI and it basically said yes
Exactly!
1:42