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visits member for 2 years, 11 months
seen 41 mins ago

Aug
26
asked Root of Unity Product
Jul
14
comment Geometry or topology behind the “impossible staircase”
+1 Very interesting.
Jul
13
comment Problem with Equivalence Relations
I'm not sure I understand your proof of symmetry. The point is that if $(x,y) \in S'$, so that $x-y = n$ is an integer, then $y-x=-n$ is an integer, so $(y,x) \in S'$. This shows symmetry. A similar comment can be made for transitivity.
Jun
10
answered Weierstrass Form of Elliptic Curve
Jun
10
answered Which one result in mathematics has surprised you the most?
Jun
10
comment Do any non-combinatorial proofs of the elementary properties of wedge products exist?
This is how John Lee does it in "Introduction to Smooth Manifolds", the book I learned from, and I think this method is very transparent. +1
Jun
8
comment Intuition behind elliptic curves and $K$-rational points
Exactly! =D A nice elliptic curve has lots of points in general...if you look at the points over $\mathbf{C}$, they form a torus, in fact, and the points on this torus have a group structure. But if we look only at points over $\mathbf{Q}$, we get a subgroup with far fewer points, and in fact the M-W theorem tells us that this subgroup is finitely generated.
Jun
8
comment Intuition behind elliptic curves and $K$-rational points
No, see my further addition. (Sorry for all the edits!) The Mordell-Weil group is the group $E(K)$. In the example at the bottom of my post, I exhibited a curve E and a point which was in $E(\mathbf{\bar{Q}})$ but not in $E(\mathbf{Q})$.
Jun
8
revised Intuition behind elliptic curves and $K$-rational points
added 250 characters in body
Jun
8
revised Intuition behind elliptic curves and $K$-rational points
added 18 characters in body; added 181 characters in body
Jun
8
answered Intuition behind elliptic curves and $K$-rational points
Jun
8
awarded  Critic
Jun
8
comment Why do books say “of course” it's never that simple, differential equations?
@Arturo: That is my thought as well.
Jun
8
answered Unique Groups for Game Tournament
Jun
8
comment Unique Groups for Game Tournament
@JasCav: I'm working on writing up the brackets that Gerry's method gives you. Stay tuned!
Jun
8
comment Unique Groups for Game Tournament
Wow, this is incredibly slick! +1
Jun
7
awarded  Enlightened
Jun
7
awarded  Nice Answer
Jun
7
comment Help on notation: $\mathbb{Z}/n\mathbb{Z}$ vs. $\mathbb{Z}_n$
Good points, all. As long as authors are explicit at the offset about what notation they are using, I guess it needn't cause any confusion. As always, context is key.
Jun
7
comment Help on notation: $\mathbb{Z}/n\mathbb{Z}$ vs. $\mathbb{Z}_n$
I agree! Another notation which I don't often see, but which I sort of favor, is $\mathbf{C}_n$ for the cyclic group of order n. It has the same brevity as $\mathbf{Z}_n$ without the confusion. Unless $\mathbf{C}_n$ is used for something else, too...?