ratchet freak
Reputation
1,497
Top tag
Next privilege 2,000 Rep.
 Jul 12 comment How to prove that the Fibonacci sequence is periodic mod 5 without using induction? @lulu but you can know the max period is 25 because that's how many pairs of numbers there are mod 5. Jul 12 comment How to prove that the Fibonacci sequence is periodic mod 5 without using induction? No-one used the closed form and expanded it out in the answers? Mar 6 comment How is another root -i? @SophieClad that is only true of quadratic equations with coefficients in R Jan 9 comment Why is inverse of orthogonal matrix is its transpose? actually it's not: [[2,0][0,2]] is orthogonal but its inverse is [[0.5,0][0,0.5]]. I think you mean orthonormal Nov 13 comment Why is the absolute sign needed in the definition of a bounded function +1 for going to the intent of the notation Aug 29 comment finding volume of the cone by using the dot product @harry it's actually $u \angle v$ Aug 29 comment finding volume of the cone by using the dot product the sine and cosine of the angle between $u$ and $v$ resp. Aug 27 comment Evaluating $\ln(\cos x))$ using Taylor expansion you should be using different unknowns, now the $x$ in the $\ln$ expansion is different from the $x$ in $\cos x$ Jul 10 comment How to create circles and or sections of a circle when the centre is inaccessible and your print screen button doesn't work? May 19 comment Number of ways to order numbers such that greatest number proceeds smallest number which is equal to $\frac{n!}{2}$ May 16 comment Proving that all eigenvalues are $0$ bar one. it's sufficient to prove that all $Ax=a\mathbf{e}$ Apr 17 comment Why does $n^0 = 1$? there is $$n^k = \Pi^k_{i=1}i$$ but that relies on $$\Pi^0_{i=1}i=0$$ Apr 10 comment Visually deceptive “proofs” which are mathematically wrong result of the assumption that $\sqrt b \cdot \sqrt a = \sqrt{a\cdot b}$ for all reals $a$ and $b$ instead of only for positive reals Apr 7 comment Visually deceptive “proofs” which are mathematically wrong all of the answers below rely on a slight bend in a diagonal line which accounts for the missing area Mar 18 comment Minimum number of different clues in a Sudoku must resist urge to solve sudoku... Mar 13 comment Can $\frac {100-100}{100-100}=2$? or a square of a negative number; the logarithm of a negative number, those are the most common but any multivalued function can be used Mar 4 comment For all square matrices A and B of the same size, it is true that (A+B)^2 = A^2 + 2AB + B^2 @Nicholas because distributiveness works even when $AB\ne BA$ (it's not related) Feb 26 comment Interesting and unexpected applications of $\pi$ isn't this the just the series expansion of $\arctan 1$? Feb 25 comment What makes a limit 'go away'? $$\lim_{x\to ∞} f(x)+g(x) = \lim_{x\to ∞} f(x)+\lim_{x\to ∞}g(x)$$ when both limits exist. and $\lim_{x\to ∞} c = c$ so you can extract the $\frac{11}{7}$ from the limit and keep $\frac{e^x}{7}$ inside it. Feb 6 comment Is it faster to count to the infinite going one by one or two by two? it doesn't matter how far you count, you are always just as far from infinity than when you started.