23h
revised How to find last point of this triangle triangle?
added 27 characters in body; edited title
23h
revised stab(S) is isomorphic to $ S_k \times S_{n-k} $
image into text
1d
answered Confused about a solution: proving every prime ideal is maximal
1d
comment How to say this proof correctly: if d|a and d|b then d|a-b.
@PrahladVaidyanathan Could you consider making that into an answer? It seems that it wound up being the best solution for the user in the end.
1d
answered A problem on complete metric space
1d
reviewed Leave Closed How to select the right books?
1d
reviewed No Action Needed Group theory applications along with a solved example
1d
comment Blackboard bold, Bold, Fraktur, and Reserved Variable.
It is user preference based on discipline and context. Notation nazis who are convinced there is a "right notation" exist but are usually politely ignored. Just do your best to be clear to your intended audience.
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reviewed Looks OK Blocks of Pyramid Pattern Expression
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reviewed Approve For any $p,q\in\mathbb{Z}[i]$, $\mathrm{N}(\gcd(p, q))$ must divide $\gcd(\mathrm{N}(p), \mathrm{N}(q))$
1d
comment What's the algebraic closure of the quaternions?
@MannyReyes I for one don't have any idea what the proposed limit looks like. Maybe the quotients are all domains and the inductive limit is too? It would seem like a bit of a miracle if the whole thing was a division ring...
1d
comment What's the algebraic closure of the quaternions?
@AdamHughes Then maybe this really is the brick wall, since $R\langle x\rangle/(xi+ix-j)$ does not make $x$ algebraic, as was hoped.
1d
comment Abstract Linear Transformation Question
Do you know what $T^k$ means? Isn't it clear what happens each time you apply $T$?
1d
comment Gallian: is it true that the well-ordering principle can't be proven from properties of arithmetic?
If by "that" you mean the link, then yes, that is a proof of the well-ordering theorem that only relies on set theory.
1d
comment Gallian: is it true that the well-ordering principle can't be proven from properties of arithmetic?
@AnalysisIncarnate I can't offer any disproof of the existence of a proof without knowing what the axioms are that he is talking about. To successfully prove there is no proof, you'd have to give an example which isn't well-ordered by nevertheless satisfies the "arithmetic axioms" that he is talking about.
1d
comment Gallian: is it true that the well-ordering principle can't be proven from properties of arithmetic?
OK, must be a typo on his part then. The integers are of course not well ordered.
1d
comment Gallian: is it true that the well-ordering principle can't be proven from properties of arithmetic?
@AnalysisIncarnate The ring axioms for $\Bbb Z$ do not even mention order, so I can't imagine how one would talk about well ordering in any case.
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comment Prerequisites for Hartshorne: Euclid and beyond?
Hartshorne is really a wonderful author. Based on my reading, I thought it would be accessible to anyone comfortable with proof classes, and not much other prerequisite would be necessary. It probably differs from person to person, but I won't let that stand in the way of my recommendation of this book :)
1d
comment What's the algebraic closure of the quaternions?
Sebastien, you want to read this paper by Lam on the quaternions for that theorem. It's an awesome paper for anyone interested in the quaternions :)
1d
comment What's the algebraic closure of the quaternions?
I don't even know that it exists, and I have much less chance of knowing if it's finite dimensional over whatever field/division ring you are imagining.