Joshua Shane Liberman
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 Dec 28 awarded Nice Question Oct 7 awarded Notable Question Sep 24 awarded Autobiographer Jun 17 answered Area puzzle in colored triangle May 17 awarded Constituent May 10 comment proof using pigeonhole principle Playing devil's advocate, I want to pair each odd number with an even numbers and each even number with an odd, to keep the differences odd, thus the product odd. Can I do that with $\frac{n-1}{2}$ even numbers and $\frac{n+1}{2}$ odd numbers? May 7 awarded Caucus Apr 12 comment How to determine the difference Onto vs One-to-one? Is liking toast and jam enough reason for a +1? Apr 9 comment Infinite sets don't exist!? The author doesn't seem to argue that mathematicians can construct numbers like this, but takes issue that this construction requires more materials than exist in the universe, even on an atomic level. I don't need infinite sets to do that, just let $x =$ the number of atoms in the universe $+ 1$. Apr 9 comment Infinite sets don't exist!? From the article - "Mathematics that makes complete sense tends to parallel the real world and be highly relevant to it". But according to Einstein, "As far as the laws of mathematics refer to reality, they are not certain; as far as they are certain, they do not refer to reality." Feb 25 awarded Popular Question Jan 31 comment Find five positive integers whose reciprocals sum to $1$ An excellent idea. Cutting out fractions of a unit circle and passing them to the class to put back together in different ways would work really well! Dec 7 comment Scale of 0-1 change it to 1-180? Let $x \in [0,1]$. Then $y = 179x+1$. Aug 28 comment Why did my friend lose all his money? Roulette tables have a zero and a double-zero, to give the casino its only mathematical advantage. Are you sure this answer true for the MUD as given? Keep in mind, one wasn't given. Aug 17 comment Need algorithm to take “max” of scores, but with “quality” weighting Need it be complicated? I would weigh each test so that I could multiply their score by its weight. Take the maximum value of the weighted scores and see if it is higher than the target value to determine success or failure. This is akin to giving the tester a few points for taking a harder version of the test, however, and I'm not sure if I understand the objective completely... Aug 1 awarded Yearling Jul 31 comment Solving $5^n > 4,000,000$ without a calculator cough typo cough Jun 22 revised Evaluating $\frac{1}{\sqrt{4}+\sqrt{6}+\sqrt{9}}+\frac{1}{\sqrt{9}+\sqrt{12}+\sqrt{16}}+\frac{1}{\sqrt{16}+\sqrt{20}+\sqrt{25}}=?$ Added approximation. Jun 22 answered Evaluating $\frac{1}{\sqrt{4}+\sqrt{6}+\sqrt{9}}+\frac{1}{\sqrt{9}+\sqrt{12}+\sqrt{16}}+\frac{1}{\sqrt{16}+\sqrt{20}+\sqrt{25}}=?$ Jun 22 comment What is the total number of combinations of 5 items together when there are no duplicates? I think this is the most intuitive way to formualate the solution, and the $2^n$ formula is more natural than when presented in @JBC's answer.