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 Yearling
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Jan
26
comment Expected Number of Loops from $n$ Ropes
In case this helps the reader: the probability of $\frac{1}{2n-1}$ comes from having $\binom{2n}{2}$ possible pairs to tie together, only $n$ of which lead to a loop (selecting both ends from the same rope). Hence the probability of making a loop is $\frac{n}{\binom{2n}{2}}=\frac{n}{(2n)(2n-1)/2}=\frac{1}{2n-1}$.
Jan
26
comment Using Stirling's Approximation to Find Maximum
I think there must be an error in your question. The series the you have written down has no maximum since it is just the exponential function $e^x$ which has no max. en.wikipedia.org/wiki/…
Oct
28
comment Dense simple smooth immersed curves in manifolds.
@JackLee Yes. My understanding is that "simple curve" and "injective curve" mean the same thing. Unless "simplicity" does not rule out self-tangency.
Oct
27
asked Dense simple smooth immersed curves in manifolds.
May
20
comment Intuition behind independence & conditional probability
This is a great explanation. And it works where conditional probability often is undefined (i.e. when $P(B)=0$).
Mar
9
comment What is the predual of $L^1$
I think $K$ also needs to be Hausdorff no?
Feb
25
comment Any open subset of $\Bbb R$ is a at most countable union of disjoint open intervals. [Collecting Proofs]
Ok thanks for clearing that up.
Feb
24
comment If $R=K[X]/(X^n)$, can represent any element as polynomial with degree $<n$
When you quotient by $(X^n)$ you're effectively saying any time you see $X^n$ you can replace the term with 0. So all terms of degree $\geq n$ will vanish.
Feb
24
comment Any open subset of $\Bbb R$ is a at most countable union of disjoint open intervals. [Collecting Proofs]
What does "R is ccc" mean?
Feb
24
answered Any open subset of $\Bbb R$ is a at most countable union of disjoint open intervals. [Collecting Proofs]
Feb
19
awarded  Yearling
Feb
19
awarded  Scholar
Feb
19
comment Are countably infinite, compact, Hausdorff spaces necessarily second countable?
This is interesting. I didn't know that there was such a complete classification for these spaces. I'll have to do some reading up on the Sierpinski-Mazurkiewicz theorem. Thanks!
Feb
19
accepted Are countably infinite, compact, Hausdorff spaces necessarily second countable?
Feb
19
revised If the sequence $a_n$ converges to $1$ then $a_{n+1}+\frac{1}{n}$ also converges to $1$
minor
Feb
19
answered If the sequence $a_n$ converges to $1$ then $a_{n+1}+\frac{1}{n}$ also converges to $1$
Feb
18
asked Are countably infinite, compact, Hausdorff spaces necessarily second countable?
Dec
17
awarded  Caucus
Sep
29
comment Does this graph operation have a name? Subgraph join?
The motivation behind naming it a "subgraph join" was that the definition is similar to that of a graph join (second definition at this link en.wikipedia.org/wiki/Graph_operations#Binary_operations), nevertheless what you said is a good point I'll keep in mind.
Sep
27
awarded  Student