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    HarryPotter5777

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    [–] Soldier running (easy) HarryPotter5777 1 points ago in mathriddles

    Just flaired it for you; in the future, you can flair posts by clicking on the red text below the post body.

    [–] 5 Points all linked together HarryPotter5777 2 points ago in mathriddles

    Ah, I missed "curved" - yeah, definitely.

    [–] 5 Points all linked together HarryPotter5777 5 points ago in mathriddles

    Assuming distances are nonzero (and thus WLOG 1), 3 points uniquely define a unit equilateral triangle, onto which a fourth point can be added in only two locations: forming a regular tetrahedron above or below the triangle. So the remaining two points must be exactly those two. But the distances between the opposite vertices of a unit regular triangular bipyramid is √3, not 1. So no such configuration exists in 3 dimensions.

    [–] What comes next? HarryPotter5777 1 points ago in mathriddles

    This sub used to get a lot of posts of this sort (many involving actual math - that's not the issue here), and it got very tiring - we instituted a rule against such posts to the approval of many users, and I know of no regular user who has wished this were not the case. It's possible to use polynomial interpolation to fit any finite number of terms to a sequence using some polynomial rule - see for instance this.

    Zendo is there for those who do enjoy this sort of problem-solving (with the ability to gather data on arbitrary values, which makes for a more interesting and interactive discussion) while being confined to a single thread at a time.

    [–] What comes next? HarryPotter5777 1 points ago in mathriddles

    From the sidebar:

    Codebreaking and "guess the rule" type posts are not permitted; if you wish to submit such a post, do so on subreddits such as /r/puzzles.

    As such, your post has been removed.

    [–] Integer distance points HarryPotter5777 1 points ago in mathriddles

    Oh right, we just need to show it's unbounded, not that there exists a single set with infinite measure.

    [–] About how old are the original characters by now? HarryPotter5777 22 points ago in questionablecontent

    IIRC, the general consensus is something like 2-3 years by now.

    [–] Integer distance points HarryPotter5777 1 points ago in mathriddles

    Can you elaborate on that construction? I don't see how it works. Where are you adding the additional balls?

    [–] Integer distance points HarryPotter5777 2 points ago in mathriddles

    This holds over R with M=1, since we can translate any part of the set by an integer distance without changing this condition and thus replace any set with an equal-measure one entirely within [0,1).

    Thus, if our set in the plane is S, we have that along any line L the intersection of L and S must have one-dimensional measure at most 1, so we're sort of looking for a kind of reverse Besicovitch set. (The fact that statements about Besicovitch sets are infamously difficult problems in geometric measure theory makes me think this might be a rather hard problem.)

    I'm not sure how to prove things from here, but that seems promising, as

    it seems like this might be a sufficient condition for an upper bound of pi/4 - for instance, a ring shape with maximum chord length 1 always has constant area of pi/4, even though it violates the problem's condition, so this seems like a potential generalization for which this property still holds. Not sure if it's any easier to show, though.

    [–] Comic 3588: Bubbles In The Sky With Diamonds HarryPotter5777 5 points ago in questionablecontent

    2671, I think? The wiki's list of music acts referenced stops at that strip. Though the actual era of regular music references like this was pre-1000 or so.

    [–] Show the [Results] ASAP Please! HarryPotter5777 5 points ago in SampleSize

    When making a new form, in the top right there are some icons that look like this. If you click on settings, there are checkboxes here - click on the second one (they're both unselected by default).

    [–] [Academic] Exploration of Personal Identity (Everyone) HarryPotter5777 2 points ago in SampleSize

    This was fun! Having to write out answers made me do some useful thinking about the questions.

    [–] n∈ℕ, 2∤n, 5∤n. When does n have a multiple that is all 1s? HarryPotter5777 3 points ago in mathriddles

    111..1 with k 1s is equal to (10k-1)/9. If this is congruent to 0 mod n, then we have two cases: either n is relatively prime to 9 or not. In the former case, the powers of 10 are cyclic mod n (as n is relatively prime to 10 by assumption) and must at some point reach 1, so there is some k at which 10k==1 mod n. If n is not relatively prime to 9, it is 3am for some m that is. We note that appending a string of 1s to itself thrice is equivalent to multiplying by 100..00100..001, which is a multiple of 3. Thus, iterating this process enough times with the string of 1s that is a multiple of m will produce a multiple of n. So all such n meet these conditions.

    [–] Rearranging a sum HarryPotter5777 1 points ago in mathriddles

    Ah, clever; nice solution!

    [–] Rearranging a sum HarryPotter5777 3 points ago in mathriddles

    Asymptotically, the sum of the first n terms is

    [;\sum_{k=1}^{2n/3}\frac{1}{2k-1}-\sum_{k=1}^{n/3}\frac{1}{2k}=\sum_{k=1}^{4n/3}\frac{1}{k}-\frac{1}{2}\sum_{k=1}^{2n/3}\frac{1}{k}-\frac{1}{2}\sum_{k=1}^{n/3}\frac{1}{k};]

    [;=\log\left(\frac{4n}{3}\right)+\gamma-\frac{1}{2}\log\left(\frac{2n}{3}\right)-\frac{\gamma}{2}-\frac{1}{2}\log\left(\frac{n}{3}\right)-\frac{\gamma}{2};]

    [;=\frac{3\log(2)}{2};]

    Nice problem! I originally started converting it into a cubic and quickly regretted my decision.

    [–] Function f:int(sphere)→int(circle) such that |A-B| ≤ |f(A)-f(B)| ∀A,B∈int(sphere) HarryPotter5777 2 points ago in mathriddles

    In general, this sort of solution should hold for objects with differing Minkowski dimension, right?

    (Also, I've flaired your post as solved, but if you didn't consider the above solution sufficient feel free to change that back.)

    [–] Cantor-Bernstein-Schrordered Theorem HarryPotter5777 1 points ago in mathriddles

    Sorry, forgot to mention that; we assume they're each totally ordered.

    [–] Prove by induction that... HarryPotter5777 1 points ago in mathriddles

    From the sidebar:

    This subreddit is for people to share math problems that they think others would enjoy solving. It is not intended for helping students with homework problems or explaining mathematical concepts. If you are searching for such a subreddit, you should consider /r/cheatatmathhomework, /r/HomeworkHelp, or /r/learnmath.

    As such, your post has been removed.