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 Apr 12 comment Give a bijection For Q: I assume that you have already shown a bijection between Z and Q. Use that. This can be written quite neatly using the Calkin-Wilf sequence. The negative rationals are unchanged, 0 -> 1, and otherwise $q\to\frac{1}{2\lfloor q\rfloor - q + 1}$. Mar 27 comment Picking points on a sphere at random This was investigated by the inimitable Kevin S. Brown here Mar 18 answered simple question on probability… Mar 10 comment A five-digit number whose square has its last five digits equal to the number. Can you find a one digit number whose last digit is equal to the number? A two digit number? Mar 3 comment Using percentages to apply fisher's exact test As the counts become large Fisher's exact test becomes a Chi-Squared test. Feb 23 answered Proving Gale-Shapley algorithm completes in $O(n^2)$ Feb 22 comment Consider the divides-relationship on $A =\{1, 2, 3, 4, 6\}$. Use the notation $D(x, y)$ to mean $x$ divides $y$. for example 2 divides 4, 1 divides 6. Feb 20 comment Simplify $\tan \{{1\over2}\tan^{-1}x + \tan^{-1}y\}$ . Try using an identity for $\tan(a + b)$ Feb 8 comment Measurable Subsets What are bounds on $\sum |E_j \cap S_n|$? Feb 7 answered Finding $P(A \cap D)$ when $P(A), P(B), P(C), P(D), P(A \cap B), P(A \cap D) + P(B \cap C)$ is known Feb 5 comment Finding $P(A \cap D)$ when $P(A), P(B), P(C), P(D), P(A \cap B), P(A \cap D) + P(B \cap C)$ is known Draw the simplest Venn diagram that has nontrivial values for the above, and see what you can manipulate while keeping the values constant. Jan 31 comment can we find a $k_4$ colored with 1 color in a $k_8$ which is colored with just 2 colors? What is the minimum size of a set of edges such that each $K_4$ contains at least one edge in the set? Jan 28 awarded Tumbleweed Jan 21 asked Induced subgraphs of a hypercube Jan 20 comment How can I tell which one of these numbers is greater? Your sum is less than 9E99 times $(9E99)^9$. This should give you a start Jan 14 comment Spivak's Limit Example Pay close attention to the difference between < and $\le$ in the definition. Understand that $0<|x-a|$ means that $x\ne a$. (This is going to continue to be important in analysis.) Jan 10 revised How was the expression relating two general solutions to $x\frac{\partial u}{\partial x}+2\frac{\partial u}{\partial y}- 2u = 0$ obtained? added 212 characters in body Jan 10 answered How was the expression relating two general solutions to $x\frac{\partial u}{\partial x}+2\frac{\partial u}{\partial y}- 2u = 0$ obtained? Jan 10 comment Continuity at a point. Are you sure it is true for all $m$ and $n$? Hint: $x^3$ is odd. Jan 10 comment How was the expression relating two general solutions to $x\frac{\partial u}{\partial x}+2\frac{\partial u}{\partial y}- 2u = 0$ obtained? Equate the two solutions.