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12h
answered Casino turns 50% of your losses into “free play”, are odds in your favor?
21h
comment Difficult sequence puzzle
I just typed 1,1,1,1,1,691,2,3617 into Google and the OEIS entry came up.
1d
comment What do the symbols $\mathbb{Z}$ and $\mathbb{Z}_n$ mean on this discrete math problem?
You can search the web for $\LaTeX$ help. I would claim the single arrow is ambiguous between the domain and range of a function and implies. $\LaTeX$ renders \implies as a double arrow $\implies$ . I am certainly not a good source for the proper formatting of arrows.
1d
answered More than 4 at Even throw of Fair Dice
1d
comment What do the symbols $\mathbb{Z}$ and $\mathbb{Z}_n$ mean on this discrete math problem?
Do Zev Chonoles' recent edits answer your question? You need to understand "integers mod $n$". That is the point of the exercise.
1d
answered What do the symbols $\mathbb{Z}$ and $\mathbb{Z}_n$ mean on this discrete math problem?
1d
answered Proving inequality involving real numbers
1d
comment Probability of a dice game: win, lose or draw.
What have you tried? Note that these rolls are just like flipping a coin, as even and odd each have probablity $1/2$ There are only three possible outcomes, so write them all down and assess the probabilities.
2d
comment Laplace transform: $y"+6y'+25y=100\sin(10000t)$
What have you tried? What did you get when you took the Laplace transform?
2d
answered A supposed to be easy calculus problem
2d
answered How to write the set of all permutations on a set $n=\{1, 2, \ldots, n\}$
2d
comment Find the solution to the initial value problem $\overline{x}' = A\overline{x}, x(0) = \begin{bmatrix}{2} \\ {28}\end{bmatrix} $
If you plug $t=0$ into your solution, you get $\overline x(0) = \begin{bmatrix}{2} \\ {36}\end{bmatrix}$, so it is not correct. As you did not show the solution, we can't find the error. If you just type eigenvalues into the box in Alpha it gives you a box below with a sample matrix that shows the format. It agrees with your double eigenvalue of $8$
2d
comment Having two random generated natural numbers between 1 and 255, and generate out of it natural number between 1 and 256
This gives $1/255$ chance of $256$ and $1/255-1/(255^2)=624/65025$ for all the rest. This is very close. If you want exact, you will need to have a chance of rerolling as $256$ is not a divisor of the $255^2$
May
19
comment Help with a proof of pairs of real numbers
@Théophile: You are right. I have deleted my comments.
May
19
comment Is the closure of $\mathbb Q \times \mathbb Q$ equal to $\mathbb R \times \mathbb R$?
Yes. If you want to be formal it takes a bit of doing, just chasing the error bounds. I like to see $\epsilon - \delta$ proofs as challenge-response. You claim your sequence in $\Bbb Q \times Q$ approaches $(x,y)$ I challenge you with an $\epsilon$ and you have to find an $N$ such that all terms after $N$ are within $\epsilon$ of $(x,y)$. You have been told that the sequence you used approaches $x$, so you can challenge whoever gave it to you to find an $N'$ such that all terms after that are within $\epsilon'$ of $x$. If you choose $\epsilon'$ well, and similar for $y$...
May
19
answered Is the closure of $\mathbb Q \times \mathbb Q$ equal to $\mathbb R \times \mathbb R$?
May
19
comment $1989|n^{n^{n^{n}}} - n^{n^{n}}$ for integer $n \ge 3$
$n=5$ is not a counterexample.
May
19
comment Prove that $1989|n^{n^{n^{n}}} - n^{n^{n}}$
This is not correct. Alpha gives $5^{5^5}\equiv 14 \pmod {17}$
May
18
comment Find the first Poulet number
One sample is to ask if $15$ divides $2^{14}-1=16383$ It does not. In general $3$ divides $2^{2k}-1$ and does not divide $2^{2k+1}-1$, so if $3$ is a factor of $n$, then $n$ must be even. This will eliminate a fair number of potential $n$ less than $341$
May
18
answered Question on rounding off rule