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21h
comment Is the Jaccard distance a distance?
Howver, the proof can be salvaged. Just define $i(A)$ to be the first element of $A$, $i(B)$ to be the first element of $B$, etc. Define $p_{A,B}$ as "$i(A)\neq i(B)$", and so on.
21h
comment Is the Jaccard distance a distance?
The definition of $p_{A,B}$ is asymmetric in $A$ and $B$, unlike Jaccard distance. The error in the proof occurs in "we look at the first element which in in $A\cup B$" since the first element which is in $A\cup B$ might be in $B$, but not in $A$; even though the first element in $A$ is also in $B$.
2d
reviewed Leave Closed Finite dimensional invariant subspaces of $C^\infty(S^2)$ under rotations
Jun
29
reviewed Close Find the expectation of function of binomial random variable
Jun
23
comment Order of vanishing of an integer polynomial at a point
@joro You are right. I feel that this is an indication that I did not ask the right question. Probably I should go back, and think what question I really should have asked.
Jun
23
reviewed Approve Hodge–Tate structures of modular forms
Jun
22
comment Order of vanishing of an integer polynomial at a point
@joro Yes, f(1,1)=1.
Jun
22
comment Order of vanishing of an integer polynomial at a point
This is very nice and helpful! This shows a direction to get what I want.
Jun
22
comment Order of vanishing of an integer polynomial at a point
@joro No, it is not a counterexample since I require $f(\alpha)=0$ and $f(1,1)=0$. If $\alpha=(1,1)$, these are incompatible.
Jun
22
comment Order of vanishing of an integer polynomial at a point
@Hacon Thanks for the reference! However, it is all over $\mathbb{C}$. Is there a version over $\mathbb{Q}$ or $\mathbb{Z}$?
Jun
22
comment Order of vanishing of an integer polynomial at a point
@JoeSilverman The case of transcendental $\alpha_i$'s is actually the easier case. Indeed, then the ideal of polynomial relations that $\alpha_i$'s satisfy is principal, say $I=(h)$, and $f$ vanishes to order $m$ iff $f$ is divisible by $h^m$.
Jun
22
asked Order of vanishing of an integer polynomial at a point
Jun
21
reviewed Close Reference request: a combinatoric result
Jun
20
accepted How slowly can a power of an ideal grow?
Jun
20
comment How slowly can a power of an ideal grow?
Nice! I believe that your deleted argument shows that if $D(I)\geq 2$, then $\lim D(I^n)/n>1$. So, as @YCor says, it might be worth undeleting it.
Jun
20
awarded  Nice Question
Jun
19
comment How slowly can a power of an ideal grow?
@YCor No, I do not even know this for $n=2$.
Jun
19
asked How slowly can a power of an ideal grow?
Jun
17
reviewed Close Non-standard naturals and goodstein sequences
Jun
16
reviewed Close A simple question on conditional expectation