André Nicolas
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 Jun17 comment Is there a questionned ordering symbol like the questionned equality? Is $\overset{?}{\text{better}}$ really better? Jun17 comment Find the value of a so that the 2 x 2 matrix A is invertible Yes, using the determinant is a good idea, particularly for a $2\times 2$ where computation is simple. Jun17 comment dividing 40 players into pairs Once we choose the rooms to be occupied by the offense, we must assign offensive players to rooms and bunks. What we need to do is make sure that in numerator and denominator we are counting the same sort of thing. Since I am using $40!$ (all permutations) in the denominator, I must have all "favourable" permutations on top. We took a counting approach since that's the sort of thing you were using. But note that Ross Millikan's direct solution is in my opinion better. Jun17 comment Prove some number is algebraic over a field I noticed that I used $5$ and $2$ instead of $5$ and $3$. That changes the hint to $\frac{2}{\sqrt{5}+\sqrt{3}}=\sqrt{5}-\sqrt{3}$. Jun17 comment Prove some number is algebraic over a field @user157243: You are welcome. There are plenty of answers already, I just wanted to give you a start. Jun17 answered dividing 40 players into pairs Jun17 comment Prove some number is algebraic over a field For the equality, clearly $\mathbb{Q}(\sqrt{2}+\sqrt{5})\subseteq \mathbb{Q}(\sqrt{2},\sqrt{5})$. For the other direction, note that $\frac{3}{\sqrt{5}+\sqrt{2}}=\sqrt{5}-\sqrt{2}$. Jun17 comment Analysis of how-many-squares and rectangles are are there on a chess board? Do you mean how do we prove that $1^2+2^2+\cdots+n^2=\frac{(n)(n+1)(2n+1)}{6}$? Many ways. Induction is one. Exploiting the fact that $(k+1)^3-k^3=3k^2+3k+1$ is another. Must have been done many times in many ways on MSE. Jun17 comment How to get the number of ways of getting a five card hand that is a straight flush from a standard deck of cards Note that definitions can differ. Wikipedia in its definition section includes the Royal flush among the straight flushes. That gives $40$. But someone else could be using a different definition. Jun17 comment Combinatorics and Probability Problem Concerning Poker Hands In a straight, the low card takes on any one of $10$ values, Ace, 2, 3, 4, 5, 6, 7, 8, 9, or 10. The highest possible low value is 10, because that gives 10, Jack, Queen, King, Ace. Jun17 comment Cardinality of all inverse functions (bijections) defined on: $\mathbb{R}\rightarrow \mathbb{R}$ There are many others that would work. I was trying to get a sort of "indicator" (yes/no) function. Don't flip if yes, flip if no sounded like a good idea. Jun17 answered Cardinality of all inverse functions (bijections) defined on: $\mathbb{R}\rightarrow \mathbb{R}$ Jun17 comment Probability- What percentage answered ‘Yes’? Hint: How many percent replied no to both? How many percent replied yes to both? If the answers are not clear, draw a Venn diagram. Jun17 comment what is inverse of $y = 5 ^ {\ln x }$ Do not use logs to base $5$. Write $\ln y=(\ln x)(\ln 5)$, solve for $\ln x$, then take the exponential. Jun17 comment instantaneous velocity Yes, you then went on to try to find the average velocity, which is not correctly done. The average velocity is the change in displacement divided by the change in time. But you already had the instantaneous velocity. Jun17 comment statements about summation I assumed that OP saw that one needed $\sum_1^\infty (\cos(k\theta)+i\sin(k\theta))$, and worried about separating into two sums. But the wording is definitely not clear enough for this to be anything more than speculation. Jun17 comment instantaneous velocity It asked for instantaneous velocity. That's $f'(1.8)$. Jun17 comment Undecidable sentence in Godel's incompleteness theorem The result about Hilbert's 10th problem is proved via an elaborate translation into "Diophantine" language of undecidability results obtained via diagonalization. Jun17 answered Need an example of piece wise function continuous but not differentiable Jun17 comment The prime elements of the ring $\mathbb{Z} \! \left[ \dfrac{i \sqrt{3} - 1}{2} \right]$. For information and references, please see this Wikipedia article on Eisenstein primes.