How does an alg affect the cube? (Full and complete answer please)

[Stefan]

To reach a better understanding of the cube.

You don't gain anything and you do lose meaning, how is that better?

The fact that you recognised my falicy means that you undertand the logic I'm trying to grasp.

I might understand what you're trying to grasp, but I don't understand what you said there. All that R = (25,27,32,30) = D etc makes no sense to me, especially because of the contradictions. Your notation is really weird, and the flawed renaming doesn't help at all.

 

[whauk]

you want some more "mathematics"? then stop renaiming everything to some disgusting sequences of numbers, letters etc. nobody wants to read this. imo this "mathematical" explanation should dispel any doubts: let the cube group be <U,R,L,D,F,B>. then compose some of the generators and it will give you another element of the cube group. (always the same since thats how a group works). then grab a real cube, execute your algorithm and voila: there you know how your new element looks like.
do you want to proof more? i cant imagine what...

 

[Lucas Garron]

you want some more "mathematics"? then stop renaiming everything to some disgusting sequences of numbers, letters etc. nobody wants to read this. imo this "mathematical" explanation should dispel any doubts: let the cube group be <U,R,L,D,F,B>. then compose some of the generators and it will give you another element of the cube group. (always the same since thats how a group works). then grab a real cube, execute your algorithm and voila: there you know how your new element looks like.
do you want to proof more? i cant imagine what...

*Unfortunately*, that's not nearly enough if you, say, want a way to tell whether two algs are the same without executing them, or want a computer to find algorithms for you, or if you want to find some property like God's number. Group theory is not for everything, but it's often very useful to have numerical descriptions.

 

[qqwref]

This is another great answer! Could you prove this answer using an "If... than..." statement where:

Given: (v,r,w,s)

V = (0,0,0,0,0,0,0,0) <-Orientation of the corners
R = (n_Sub_0,n_sub_1) <-Permutation of the corners
w = (0,0,0,0,0,0,0,0,0,0,0,0) <-Orientation of the edges
s = (I_Sub_S_Sub_12) <-Permutation of the edges

is the Identity element?

It looks like you think you are asking for a more "mathematical" answer, but you're actually asking for an answer where everything is written out in full, wasting space and making it much more hard to understand. You want an intuitive explanation of why the algorithm does what it does, don't you? Because this wouldn't help.

All that stuff you were talking about earlier with permutations of numbers from 1 to 48 will actually give you zero extra knowledge. All you'd do to "prove" the sequence works is to write out what each turn does, combine them together, and then see what the end result is. But that's exactly the same thing you'd get if you just performed the sequence on the cube and traced each sticker separately with one finger. All you'd be doing is simulating a cube on paper with numbers, which takes longer and gives the same rsult. Permutations can be a very useful tool for analyzing things, but as it turns out everyone on the forum has a real-life model of a permutation group, so there's no need to ever have the permutation itself written out unless you are a computer program (such as GAP, or a cube solver).


PS: You know, our forum actually has a TeX thing You can use the \( tag, i.e. \( f(x) = x^2 \). \)