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6h
comment Choosing randomly integers from $1$ to $10$
Where did you get $3/10$, and why are you multiplying it with itself?
23h
answered $0,1,0,1,0,1$… has only $2$ limit points
1d
comment $45^\circ$ Rubik's Cube: proving $\arccos ( \frac{\sqrt{2}}{2} - \frac{1}{4} )$ is an irrational angle?
There's a proof at arxiv.org/abs/1006.2938. Someone might want to write it up as an answer...
Jun
30
comment How to derive $\sum_{n=0}^\infty 1 = -\frac{1}{2}$ without zeta regularization
You're addressing the alternating series $1-1+1-1+\cdots$, but the OP asked about the positive series $1+1+1+1+\cdots$. The latter is not Cesaro or Abel summable.
Jun
30
comment Interpretations of divergent series
Note that your geometric interpretation only applies to the sum of an absolutely convergent series, which is the limit of the entire net of partial sums over arbitrary finite sets of indices. As soon as you consider the classical sum, which requires only a limit of a sequence of consecutive partial sums, you've already left behind that geometric interpretation! So before you ask about divergent series, it would be useful to figure out what kind of interpretation you would accept for a conditionally convergent series.
Jun
29
answered Which of $(-\infty,\infty]$ and $[-\infty,\infty]$ is homeomorphic to $S^1$?
May
30
answered Why multiplying those 2 quaternions doesn't give the expected result?
May
30
comment modelling the behavior of a particle
Could you give an example of the kind of state representation you're thinking of? The description "doing a linear transformation" could potentially mean lots of different things.
May
30
revised Category theorem
edited tags; edited tags
May
30
comment Prove or disprove $\int_{-\infty}^\infty \frac{dx}{\cos x+\cosh x}=\frac{1512835691 \pi}{1983703776}$
@bof Interesting question! I'm not an expert on this, but I suppose Dirichlet's approximation theorem tells us that it's common to get $2N$ digits from an $N$-digit denominator.
May
29
comment Impossible Math Riddle
Also math.stackexchange.com/questions/581225/what-are-the-ages, and see similar math.stackexchange.com/questions/40158/…
May
29
comment Are the irrationals + zero an additive group?
See also math.stackexchange.com/questions/157245/… and math.stackexchange.com/questions/867569/…
May
28
comment minimal embeddings of topological spaces into connected spaces
...oh actually, you said a one-point compactification, not the one-point compactification. Never mind then. :)
May
28
comment minimal embeddings of topological spaces into connected spaces
By the way, it isn't quite right to call this the one-point compactification of $X$. In a one-point compactification, the added point typically does have neighborhoods that aren't the whole space. It happens that the one-point compactification of $\mathbb Q$ is also connected, so it's another good example.
May
28
comment minimal embeddings of topological spaces into connected spaces
In the terminology of Steen and Seebach's Counterexamples in Topology, this is the open extension of $X$. They also note that it is connected, as reflected at proofwiki.org/wiki/Open_Extension_Space_is_Connected
May
28
comment How do we add numbers?
(Well, if a pile of rocks is considered an acceptable encoding of a number, then we can just lump the piles together with a bulldozer to compute the sum!)
May
27
comment Determinant of symplectic matrix
@RSG Sorry, I've long since forgotten what little I once knew on the topic. :) You might want to raise another question with tag:reference-request for that.
May
27
comment Determinant of symplectic matrix
For future reference, these are related questions without any constraints on the method of proof: math.stackexchange.com/questions/242091/… math.stackexchange.com/questions/501130/… math.stackexchange.com/questions/930319/…
May
27
answered Determinant of symplectic matrix
May
27
answered Squares in $\mathbb Z_p$