JeffE
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 Jan 25 comment Is computer science a branch of mathematics? computer scientists who know little about computers. — It would be more accurate (and less insulting) to say "computer scientists who care little about computers", but even that would be an exaggeration. Mar 29 comment how to prove function satisfy Lipschitz condition Simultaneously cross-posted on cstheory.SE. Don't do that. Feb 5 comment Gerrymandering on a high-genus surface/can I use my powers for evil? I think there's an implicit assumption that at most two roads can meet at any overpass. Even in the real world, each overpass intersects at most a constant number of roads. Sep 14 comment If $f(n) = \sum_{i = 0}^n X_{i}$, then show by induction that $f(n) = f(n - 1) + X_{n-1}$ Why isn't "That's the definition of $\sum$." the complete proof? Sep 14 comment Supremum and infimum of $\{\frac{1}{n}-\frac{1}{m}:m, n \in \mathbb{N}\}$ Do you mean A has only one element (which is what you've written), or do you actually mean $A = \{1/n - 1/m \mid n,m\in\mathbb{N}\}$? Jul 31 comment For what values for m does $\sum \limits_{k=2}^{\infty}\frac{1}{(\ln{k})^m}$ converges? I suggest defining $\ln^+ n = \max\{\ln n, 1\}$ and then replacing all $\ln$s with $\ln^+$s. Jul 27 comment difference between graph and multigraph Isn't every graph trivially a multigraph? Jul 1 comment Equality of Voronoi diagram @fog: I assume by "denotes" you mean "implies". Jun 25 comment Equality of Voronoi diagram On the other hand, any Voronoi diagram with at least one vertex is generated by a unique set of sites. So if there is at least one Voronoi vertex, you really do have $A=B$. Jun 9 comment mathematical notation for a logical statement "and" is even better than $\land$. Jun 9 comment maximum flow ford-fulkerson analysis No, if (a,b) is in E, then both (a,b) and (b,a) are in E'. In particular, E' is always a superset of E. On the other hand, $|E'| \le 2|E|$, so $O(E') = O(E)$. May 31 comment How does one give a mathematical talk? It. Is. Not. Possible. To. Speak. Too. Slowly. May 29 comment Where/What are good sources to learn about the history of computation? That said, I think the question is much too broad. Do you mean computing devices (starting with Stone Age tally sticks, or even fingers), or algorithms (starting perhaps with techniques that were already centuries old when they were described in the Rhind Papryus), or applications (starting perhaps with agriculture)? May 29 comment Where/What are good sources to learn about the history of computation? @Gigili: Cross-posting is generally discouraged; migration might be a better option if the question doesn't get good answers here. See this discussion at meta.cstheory. May 24 comment Determining position at some point in time Hint: This should have the computational-geometry tag. May 21 comment Variety vs. Manifold Even in French, a red herring is neither necessarily red nor necessarily a fish. (And no, @Galoisfan, the phrases "algebraic variety" and "algebraic manifold" are not synonyms, even in English; read the answer again!) May 20 comment Expected Number of Convex Layers and the expected size of a layer for different distributions Well, that's just a back of the envelope estimate. It might be good for intuition, but I wouldn't trust it to give a precise bound, especially after several iterations. May 19 comment Expected Number of Convex Layers and the expected size of a layer for different distributions But $P_1$ is not uniformly distributed in a square; it's uniformly distributed in $conv(P)$, which has $\Theta(\log n)$ sides in expectation. So the right back-of-the-envelope estimate for the complexity of the convex hull of $P_1$ is $\Theta(\log^2 n)$. More generally, deeper layers are "rounder", and boundary effects matter less. May 17 comment Can every nonsingular $n\times n$ matrix with real entries be made singular by changing exactly one entry? @ZevChonoles: Yes, much better. (You can't make the identity matrix singular by changing an off-diagonal entry, for precisely this reason.) May 17 comment Can every nonsingular $n\times n$ matrix with real entries be made singular by changing exactly one entry? But what if the coefficient of $a_{k\ell}$ is zero? Equivalently, what if the function $f$ such that $\det(A) = f(a_{k\ell})$ is actually constant?