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Sep
17
answered Is the Riemann sphere homeomorphic to $\overline{\mathbb{R}}\times\overline{\mathbb{R}}$?
Sep
8
comment Determinant - derivation of the general formula and its history
Note that there are several (equivalent) methods of defining and computing the determinant of a matrix. See this post, this post, and this post for some answers to your questions.
Sep
7
revised How to find out when the profit of a transaction will hit $500,000
edited tags
Aug
29
comment Spherical geometry as an example of non euclidean geometry
@Paprika To identify antipodal points is OK today, but would in ancient times violate the definition of a point ("that which has no part"). I agree that spherical and Euclidean geometry differ significantly, and that to bridge these differences you have to rework your definitions and foundations, which goes a long way of explaining why it took so long time.
Aug
28
comment Solve this number theory problem without plugging in
(1) If $a=0$, $b=-1$, $c=0$ then $ac<b^2$, making your statement false instead of true. (2) But if $a,b,c$ represent different integers, you cannot have both $a=0$ and $c=0$. (3) For the statement to be true, you must show that it holds for all choices of $a,b,c$. For the statement to be false, it is enough to fine one counterexample.
Aug
28
comment how to fairly select a leader
@HagenvonEitzen The natural extension would be to permit any convex combination of any set of votes that you are unable to decide between.
Aug
28
comment how to fairly select a leader
@flawr In your suggested method, note that there is no difference between distributing 2,1,0,0 points to the four candidates and distributing 3,2,1,1 points instead. What happens is that these voters are not able to punish their worst candidate as much as the other voters.
Aug
28
comment how to fairly select a leader
@flawr Assuming the Borda count method is used, this would be correct. A voter voting in this way is essentially saying: "I have no idea what to do about $d$, so I put $d$ in the middle and let the others decide where $d$ should end up."
Aug
28
comment how to fairly select a leader
The condition Independence of Irrelevant Alternatives in Arrow's theorem is very strong, and most election methods used in practice do not satisfy it.
Aug
28
answered how to fairly select a leader
Aug
23
comment Directly prove that $2x^2 -4x + 3 > 0$ for all real $x$
The technique is called completing the square.
Aug
23
comment Can we get just $3$ from $\pi$?
How about $\pi(5)$, where $\pi$ is the prime-counting function?
Aug
23
comment Polydisc is not biholomorphic to any strictly pseudoconvex domain
@Math Make a holomorphic change of coordinates so that $D$ becomes strictly convex near $\phi(0)$, locally given by $y_2<h(x_1,y_1,x_2)$ where $h$ vanishes to second order. Compose $\phi$ with the projection on the second coordinate $z_2$. The result is a one-variable holomorphic map which maps the interior point $0$ to a boundary point of its image, and such a map has to be constant.
Aug
22
revised Polydisc is not biholomorphic to any strictly pseudoconvex domain
deleted 1 character in body
Aug
22
comment History of notation: “!”
@TonyK Cajori agrees with Hilbert that it should be $\underline{\big|n}$. He also says this notation was introduced in 1827, and became somewhat popular only after Todhunter used it in his texts around 1860.
Aug
22
answered Polydisc is not biholomorphic to any strictly pseudoconvex domain
Aug
22
comment Notation problem in integration: write $dx$ or ${\mathrm{d}}x$?
@ChristianBlatter I think not, but I see the Cambridge typesetting standard disagrees with me. From this description of the ISO standard, "italic symbols should be used only to denote those mathematical and physical entities different values," and "Any other symbol that was not dealt with in the preceding section must be set in roman font". It is my interpretation that if something cannot assume different values then it is because it is the name of something.
Aug
21
revised Notation problem in integration: write $dx$ or ${\mathrm{d}}x$?
added 2 characters in body
Aug
21
answered Notation problem in integration: write $dx$ or ${\mathrm{d}}x$?
Aug
20
awarded  Nice Answer