Jan Dvorak
Reputation
581
Top tag
Next privilege 1,000 Rep.
Create new tags
 Jan 10 comment How many sequences of rational numbers converging to 1 are there? You have demonstrated there is at least a continuum of such sequences. Can you provide an upper bound? Dec 31 comment V.I. Arnold says Russian students can't solve this problem, but American students can — why? @ian indeed, but integer-sized legs are what most students expect. Not valid reasoning, but some students might have followed it anyways. Dec 31 comment V.I. Arnold says Russian students can't solve this problem, but American students can — why? @user but none of them have integer-sized legs Dec 31 comment V.I. Arnold says Russian students can't solve this problem, but American students can — why? An easier proof would be to draw a Thales' circle around the hypotenuse and note that it has no point 6 inches away from the hypotenuse. Dec 27 comment Past open problems with sudden and easy-to-understand solutions Consider the Collatz' conjencture. It has been open for decades, and yet it has a very simple solution. We just don't know what the solution is. Dec 19 comment Is a function that maps every compact set to a compact set continuous? My mistake. A function that's locally continuous everywhere is continuous. OTOH there is a difference between locally monotonous everywhere and monotonous globally. There is also monotonous on every defined interval, which is again slightly different. Dec 19 comment Is a function that maps every compact set to a compact set continuous? As in, every point has a continuous neighborhood Dec 19 comment Is a function that maps every compact set to a compact set continuous? Wow. This even works if you replace "continuous" with "locally continuous everywhere". Nov 5 comment Does the operation of a group matter when talking about isomorphism? Oh. The OP meant the group of non-zero real numbers. Then I agree... Nov 5 comment Does the operation of a group matter when talking about isomorphism? "For example, the only reasonable group structure on $ℝ^x$ is multiplication" - strange, I would think it's addition since per-component multiplication isn't invariant to rotations. For $ℝ^3$ we also have the cross product, but that's a special case (and so is ordinary multiplicationi n $ℝ^1$. Oct 29 comment Can four consecutive numbers all be powers of whole numbers? However, $2,3,4,5$ works if you count primes as powers of primes. Oct 22 comment Sets of Prime and Composite Numbers It can be proven that at least one of these four sets is infinite. Jun 14 comment Proof that Convex Function with alternate variable is convex There are actual horizontal lines in markdown, FYI May 28 comment How to integrate a function with a nested absolute value: $|x^2 - 2|x||$? Hint: the absolute value function is piecewise linear. Can you integrate piecewise integrable functions? Mar 16 comment Cute problem a computer science classmate shared (adding non-coprimes to n smaller than n as fast as possible) Why do I feel like the part of title that's in parentheses is way more important than the part that isn't? Feb 11 comment A ship sails to an island . Find the average sailing speed for the whole journey. How did this become a hot question??? Dec 29 comment In a room there are eight lights. Each light can be switched on and off independently of the others. In how many ways can the room be lit with-? Why not just do $8\choose 5$+$8\choose 6$+$8\choose 7$+$8\choose 8$? Dec 27 comment Is there a proof that zero multiplied by infinity = a real number Zero times infinity is undefined. There's nothing to prove here. Move on. Dec 27 awarded Civic Duty Dec 20 comment Best function getting 0 for odd parameter, 1 for even This should evaluate pretty fast: min(abs x', abs(x'-2)) where x' = x mod 2