Visual Group Theory: What is a group? (2016) [video]

Re:Visual Group Theory: What is a group? (2016) [video] by smadge on Saturday February 10, 2018 @04:22AM (#16346559)

I don't see how a permutation group lends itself well to a geometric or visual interpretation in general. From my understanding, a permutation is just a one-to-one and onto function from a set to itself. For a set of N elements there are N! possible permutations, any subset of which could be used to generate a permutation group. How do you propose to interpret all of these groups geometrically, as opposed to abstractly?

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Re:Visual Group Theory: What is a group? (2016) [video] by gowld on Saturday February 10, 2018 @11:36AM (#16348002)

The permutation group on N elements is the (N-1)dimensional simplex (1:point, 2:line, 3:triangle, 4:tetrahedron, ....)

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Re:Visual Group Theory: What is a group? (2016) [video] by smadge on Monday February 12, 2018 @01:15AM (#16356904)

So every finite group is isomorphic to a subgroup of a N dimensional simplex? And then we should build our intuition about these groups via a geometric visualization? These are not rhetorical questions, I'm currently learning abstract algebra and trying to understand.

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Re:Visual Group Theory: What is a group? (2016) [video] by ndnjjfhshhvjj on Saturday February 10, 2018 @05:46AM (#16346767)

> one-to-one and onto funktion

I don't think that's the established terminology.

> How do you propose to interpret all of these groups geometrically,

How do you not? This pure maths wank really grinds my gears. Of course you can substitute other perceptive phenomena next to the visual. But even your abstract thoughts have to be accomodated in the geometry of the brain, if you think about it.

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Re:Visual Group Theory: What is a group? (2016) [video] by filmor on Saturday February 10, 2018 @06:54AM (#16346936)

>> one-to-one and onto funktion > > I don't think that's the established terminology.

It is. Injective and surjective are more "international", but those English names are fine as well. What's missing is that the function sshould map a set onto itself.

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Re:Visual Group Theory: What is a group? (2016) [video] by smadge on Tuesday February 13, 2018 @01:47AM (#16365222)

> Injective and surjective are more "international", but those English names are fine as well

Thanks! one-to-one and onto is the terminology my American courses are using.

> What's missing is that the function sshould map a set onto itself.

Just for the record I initially stated "a permutation is just a one-to-one and onto function from a set to itself" as you say it must.

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