What is a group?

A link to the full video is at the bottom of the screen.

That video introduces group theory and the monster group.

Editing from long-form to short by Dawid Kołodziej

[Symmetryy]

Hrm... I wonder why i got this specific video

[harrytowers]

Ok but you didn’t explain the entirety of group theory in 60 seconds and I don’t know how links work!

[stoched]

You sort of explain it when you say “leave it looking the same”, but for clarification for anyone who doesn’t know - a group specifically is a set of items under a binary operation such that the result will also be part of the group (along with requirements). If you perform the operation on 2 elements of the set and the result is outside the set then it’s not a group. An example would be the set of Natural numbers under division. This would not be a group because you can divide 2 natural numbers and get a rational as a result which is not in the set of natural numbers. It also doesn’t satisfy some of the other requirements but I think that gets the point across.

[TheTexansgk]

The picture of the face would be in the group C2v because it is also symmetric about a plane that contains its primary axis of rotational symmetry. The face itself would be Cs because 3D faces don't have rotational symmetry.

[fcpjenz]

i remember this topic from my organic chemistry classes. it is incredibly interesting, how this basic concept leads to explanations concerning chemical properties of molecules…

[the.spriggan]

Ok i think now i understand a lil more about what Matt was going on about in that spacetime video about electroweak force. The U2 and SU3 symetries

[Olodus]

I love these shorts as a way for me to repeat and remember the things from your videos. That said, the audio might be a bit low. I have to really turn up the volume to hear anything.

[TheTechAdmin]

How many actions D's NUTS?!





I'm so not the person to make a joke like this but I don't know what came over me!

[happmacdonald]

This is one that would have heavily benefited from getting some re-formatting for vertical format (beyond just that one pan-and-scan-style zoom out)

[Taruntej.]

C2 is 2 folded axis of symmetry....
n=360/theta where theeta is the angle of rotation about an axis
Cn is n folded axis of symmetry

[BetaTestingUrGf]

Why do you count the "do nothing" operation? Does it solve some issue with the math? Otherwise i dint get it. Why would everything be atleast c1 symetric ?

[michaelwinter]

> Doing nothing counts as a part of the group

I’m part of the group!!

[SundersBurrito]

What would a D1 shape look like? Is it possible?

[tomking]

Crazy how almost all modern abstract algebra (groups, rings, fields, vector spaces, algebras) came from some guy saying, “But what if we pretended sqrt(-1) was a thing”

[justbram]

Where was this when I was doing my undergrad in math 😭

[wrc]

Question: if 1^x=2 (from brpr) would you (assuming the period of 0->2pi) write it as e^(0x)=2 or e^(2ipix)=2. One has a solution the other doesn’t. This works for all periods of 2pi•k. Can you show, perhaps visually, why this is?

[pulverizedpeanuts]

I think that was a group action, not a group

[Kiranfalak]

Can you please tell more about it. In a longer vedio

[skywatcher]

pretty sure you already upload this before

[nenwhwq]

Are the actions necessary some kind of symmetries?