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 Dec 2 revised Is it possible to simulate a floor() function with elementary arithmetic? typo Dec 2 comment Is it possible to simulate a floor() function with elementary arithmetic? Since all your ops are on integers, the output of each op will be integers. The default implementation of integer division and so will be to 'round to 0' which is equivalent to 'floor' on non-negative integers. Which means you don't need a special 'floor' function because you already have it by default. Dec 2 answered Is it possible to simulate a floor() function with elementary arithmetic? Dec 2 answered Is it possible to simulate a floor() function with elementary arithmetic? Nov 8 answered Reference textbook about proof techniques Nov 8 revised Reference textbook about proof techniques proof -> proofing Sep 30 awarded Explainer Sep 29 comment Why are real numbers useful? Use the binomial distribution. Sep 25 comment Understanding why Hall's marriage theorem $\Leftrightarrow$ Dilworth's theorem robertborgersen.info/Presentations/GS-05R-1.pdf gives a number of proofs around all these theorems. Sep 25 comment Analytic Proof Of ${n\choose r}={n-1\choose r-1}+{n-1\choose r}$ I would call this an 'algebraic' proof. An 'analytic' proof would more likely be a proof using generating functions. Of course everything uses algebra to some extent, but the major category of a proof is the primary strategy. Sep 25 comment Sum of sequence of cubes and summation on the upper index $k^3 = 6{k \choose 3} + 3 k^2 -2k$ (I got this by expanding out ${k \choose 3}$). Now eliminate the $k^2$ using ${k \choose 2}$. Then again for the leftover $k$ term. Now, if you sum the LHS, you sum the RHS. But by the stated thm, you can calculate the sum of the RHS. Sep 25 comment General term of $(1+x)(1+x^2)(1+x^3)…$? If you want to calculate these without calculating coeffs of the gf directly, I think the best formula is the recursive one in the OEIS: a(n)=(1/n)*Sum_{k=1..n} b(k)*a(n-k), with a(0)=1 and b(n)= A000593(n) = sum of odd divisors of n. Sep 22 awarded Good Answer Sep 20 awarded Nice Question Sep 16 awarded Yearling Sep 10 awarded Nice Answer Sep 4 answered Proof of trigonometric identity $\cot \theta \sec\theta= 1/ \sin\theta$ Jul 31 awarded Notable Question Jul 28 comment Is every factorial divisible by its sum of digits? @G.H.Faust: Add it to OEIS!! Jul 27 comment Is every factorial divisible by its sum of digits? what about sum of binary digits? (following the usual observation that there's nothing special about 10)