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dcernst / IBL-AbstractAlgebra

IBL course materials for an undergraduate first-semester abstract algebra course that emphasizes visualization.
http://dcernst.github.io/IBL-AbstractAlgebra/
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Clarification #88

Closed marcoswastaken closed 4 years ago

marcoswastaken commented 6 years ago

On first read, one might erroneously infer that the set of actions is only the set of generators.

dcernst commented 6 years ago

Sorry for the delay. I'll try to think this over tonight or tomorrow.

marcoswastaken commented 6 years ago

No problem. By the way, if there is a better way to make suggestions like this one beside by making pull requests? I am still learning the whole git process, and I don't want to step on toes.

dcernst commented 6 years ago

Doh, I dropped the ball on following up on this.

In your suggested changed you wrote: "These are all of the finite words made up of our generators." This isn't quite right. The collection of words is generally much larger than the set of net actions. Formally, a group element (or action at this point in the notes) is an equivalence class of words. Do you disagree with what I wrote or were you hoping to add clarification?

I'm not really sure what the best approach is in this case. Since I don't plan on actively developing the version you are using, I wonder if forking it and modifying to your heart's content is the best way forward. Since some other folks are using the same version, I'm hesitant to make any substantial changes unless it is to fix an error. Thoughts?

marcoswastaken commented 6 years ago

I think the main confusion I ran into was the statement: "...we must start with some fixed set of actions. These are our generators."

To me, that reads as, the set of actions is the set of generators.

I think a modification that could clear up without adding extra rules or nuance might be:

Rule 1 states that we must start with some fixed set of actions. From these, we may fix a set of generators. Not every action must appear in such a set.

As for maintaining a fork, I am fine with that. Though, once your new version is live I hope to contribute if I can.

dcernst commented 4 years ago

I'm pretty sure this is no longer relevant.