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13h
comment Is there an “interesting” function that grows faster than $n^{kn}$ but slower than $2^{2^n}$ — relates to understanding googolplex
Nothing wrong with $f(n)=n^{n^n}$, the number of ways to fill an $n$-dimensional cube of side $n$ with numbers from $1$ to $n$. You have $f(57)$ roughly a googolplex.
14h
comment Probability that a cow is black given that I've observed at least one side is black
Are you looking at the port side or the starboard side of this here cow?
1d
comment Probability that one of a set of four points lies within the triangle formed by the other three
So it's $35/(12\pi^2)$. Nice. Certainly the probability doesn't depend on the radius of the circle; the problem differs only by an overall scale factor if $r \neq 1$.
1d
comment Probability that one of a set of four points lies within the triangle formed by the other three
@DougCouchman: The four possibilities ($D$ is inside $ABC$, $A$ is inside $BCD$, etc.) are equally likely and mutually exclusive, so the probability that any of them is true is just $4$ times the probability that a particular one of them is true.
1d
answered Solve $\lfloor \sqrt x \rfloor = \lfloor x/2 \rfloor$ for real $x$
Nov
21
comment Square root of a divergent series diverges.
If $\sum a_n$ diverges, then $\sum\sqrt{a_n}$ diverges as well, but $\sum\sqrt{a_n}/n$ can converge or diverge.
Nov
21
comment Prisoners Problem
Do the prisoners know whether the earlier prisoners were executed or not?
Nov
21
comment Study the character of the series $\sum_{n=1}^{\infty} \left|\frac{1}{n^{2z}}\right|^2$
Oh, I see your point. Since $n^z$ is technically multivalued for complex $z$, you could consider other branches beyond the principal branch.
Nov
21
comment Study the character of the series $\sum_{n=1}^{\infty} \left|\frac{1}{n^{2z}}\right|^2$
I don't believe that formula is correct… $\left| n^z \right|=\sqrt{n^{z} n^{\bar{z}}}=\sqrt{n^{x+iy} n^{x-iy}}=\sqrt{n^{2x}}=n^x$, where $x=\Re(z)$. There's no dependence on $\Im(z)$ at all.
Nov
21
revised Study the character of the series $\sum_{n=1}^{\infty} \left|\frac{1}{n^{2z}}\right|^2$
added 2 characters in body
Nov
21
answered Asymptotic behaviour of a sequence with finite sum
Nov
21
comment Probability of winning first, second or third in a contest with 100 contestants
With your description of the sample space, there aren't just three possible scenarios where Michelle wins a prize: when Michelle wins first or second or third, there are $P(99,2)$ ways to fill the other two spots in the top three. So the probability is $3 P(99,2)/P(100,3)=3\cdot 99 \cdot 98 / (100 \cdot 99 \cdot 98)$, or $3/100$.
Nov
20
answered Study the character of the series $\sum_{n=1}^{\infty} \left|\frac{1}{n^{2z}}\right|^2$
Nov
19
comment circular contour integral with complex numbers
What are your thoughts? What have you tried?
Nov
19
comment Help with proving a language is regular (Sipser problem 1.49a)
As discussed in the other question you linked to: the string $1^p 0 1^p$ starts with a $1$ and then contains another $1$ later on, so it belongs in $B$ according to $B$'s membership criterion with $k=1$ (and continues to do so once it's pumped). You don't need to take $k$ as large as possible.
Nov
19
comment Calculate 1D random walk with alternating step size expected iterations to return to origin
You'd guess that the expected time to return to the origin would diverge, as it does in the usual 1D random walk.
Nov
19
comment Define another Equivalence Relation from Geometric Figure?
What do the equivalence classes (which are, after all, just sets of points) look like? Once you understand that, can you come up with a different equivalence relation where the equivalence classes look similar?
Nov
18
comment The Jugs of Water Problem - with constraints
Assuming the "amounts" need to be integers, right?
Nov
17
answered $(n!)!>n^{n!} \forall n \in \Bbb N^{\ge 4}$
Nov
16
comment If $\displaystyle \lim_{n \to \infty} |a_n - b_n| = 1$ and $ a_n$ is bounded, does that make $b_n$ bounded?
Indeed, it is sufficient for $|a_n - b_n|$ to be bounded (it doesn't even need to converge).