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Nov
25
awarded  Tumbleweed
Nov
18
asked Connection between maximizing a quadratic form and maximal variance
Nov
18
asked Intuition for the singular vectors and the outer products in SVD of a non-diagonalizable matrix
Nov
17
comment Difficulty understanding proof of Yoneda's Lemma
I was just reading about this part today. Yoneda functor. I can follow the arrows but I'm still not as comfortable as id like bookkeeping in my head the appearance of the natural transforms because of the layering (arrows on sets of arrows). I'll keep at it.
Nov
17
asked Understanding representable functors
Nov
15
comment What is the expected number of distinct drink types a group of $k$ people will order if there are $n$ choices?
got it, thanks!
Nov
15
comment What is the expected number of distinct drink types a group of $k$ people will order if there are $n$ choices?
Jack, how do you get the $j!$ in ${k\brace j}\cdot j!\cdot\binom{n}{j}$? I was reading this as choose the $j$ unique drinks in ${n \choose j}$ ways then for each of those you have $k$ people and you want to partition them into $j$ non-empty sets (stirling of second kind) which is ${k \brace j}$ but I don't see where $j!$ comes in...
Nov
15
accepted What is the expected number of distinct drink types a group of $k$ people will order if there are $n$ choices?
Nov
15
comment What is the expected number of distinct drink types a group of $k$ people will order if there are $n$ choices?
Yes! This agrees numerically in R with the $M^{k-1} \cdot 1:k^t$
Nov
15
comment What is the expected number of distinct drink types a group of $k$ people will order if there are $n$ choices?
You're right, in that case it's not straightforward to me how to express an exact probability for $i$.
Nov
15
revised What is the expected number of distinct drink types a group of $k$ people will order if there are $n$ choices?
added 172 characters in body
Nov
15
asked What is the expected number of distinct drink types a group of $k$ people will order if there are $n$ choices?
Nov
15
comment Difficulty understanding proof of Yoneda's Lemma
Let us continue this discussion in chat.
Nov
15
revised Difficulty understanding proof of Yoneda's Lemma
deleted 235 characters in body
Nov
15
revised Difficulty understanding proof of Yoneda's Lemma
deleted 235 characters in body
Nov
15
comment Difficulty understanding proof of Yoneda's Lemma
It kinda helps to think of $\Phi$ as a collection of maps, yes. And I understand how by defining $\Phi_A$ on (the map between $Hom(A,A)$ and $F(A)$) on $id_A$ we fully establish $\Phi_X$ (the map between $Hom(A,X)$ and $F(X)$) for any $f$. What I'm trying to do now is see if this gets us a commutative square involving $Hom(A,X), Hom(A,Y), F(X)$, and $F(Y)$
Nov
15
comment Difficulty understanding proof of Yoneda's Lemma
I don't know how either, I think I've updated my question to agree with your Point 2. $f_*(id) = f$ is true, yes. I think what I don't get is $\Phi$ - it's some "higher level" abstraction so I'm having trouble extending the logical consistency of the inner square above to arbitrary $X,Y$ and visualizing all of $\Phi$
Nov
15
awarded  Editor
Nov
15
comment Difficulty understanding proof of Yoneda's Lemma
@peterag, I updated my question to take into account my latest understanding as I keep thinking about this.
Nov
15
revised Difficulty understanding proof of Yoneda's Lemma
further understanding