This page doesn’t disambiguate between “left inverse” and “inverse”. Strictly an “inverse” is a two-sided inverse, so gf = 1 and fg = 1.
Patrick Stevens
Karma: 24
A question about the requisites for this page: should the alternating group on five elements is simple be a requisite? It’s necessary for the base case of the induction, but one can probably understand the proof without it, simply referring to it as a known fact.
I think this probably wants a diagram of the two graphs, being differently laid out in the plane but isomorphic.
This is definitely a page which admits two lenses: the “easy” proof and the “theory-heavy” proof. What kind of lens design might people use?
“identity” is probably not a sufficiently specific link; I’d go for math_identity, probably.
I feel like symmetric_group should be a requisite for this page. However, this page is linked in the body of symmetric_group, so it seems a bit circular to link it as a requisite. I think this situation probably comes up for most child pages; what’s good practice in such cases?
None that I’m aware of, but I’ve found it convenient to know when I was doing exercises in a first course in group theory.
I took the plunge and put it on its own page.
Request for comment: is the definition of “cycle” something that should be on its own page? They’re not about the symmetric group per se, but I’ve only heard of cycles being used in the context of symmetric groups.
I have a question about general Arbital practice here. A mathematician will probably already know what a group homomorphism is, but they probably also don’t need the proofs of the Properties, for instance, and they don’t need the explanation of the trivial group. Should I have split this up into different lenses in some way?
To the original author: xkcd images are CC BY-NC (2.5), and as such require attribution.