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3m
comment What is the highest number that can be got from 4383 by moving exactly 2 matches?
@PedroTamaroff -- Oops, thanks -- corrected now with only two matches moved.
4m
revised What is the highest number that can be got from 4383 by moving exactly 2 matches?
edited body
11m
answered What is the highest number that can be got from 4383 by moving exactly 2 matches?
2h
comment Of strings and substrings: A problem of probability
Your notation/terminology seems confused, but I suspect you are considering $X$ to be a random variable with values in $\Sigma^*$. Then if $X_1, ..., X_n$ are i.i.d., each with the the same distribution as $X$, one can consider the distribution of the concatenation $Y = X_1...X_n$, and of functions such as $C(x,Y)=$ the number of substring occurrences of $x$ in $Y$, etc.
1d
comment Is there a number so large that we could never calculate it?
@EricWofsey - I would rather say "Not being able to prove the decimal expansion of a number from some definition doesn't necessarily have anything to do with size." For your definition of $x$ it may not, but for the definition of $\Sigma(10\uparrow\uparrow 10)$ it evidently does (as per the sources cited above).
1d
awarded  Nice Answer
Jul
26
comment Is there a number so large that we could never calculate it?
"That [there are numbers that can’t be computed] is exactly what I'm talking about!" -- But note that the uncomputability of a real number is not related to its magnitude. E.g., "almost all" of the uncountably many real numbers in the interval $(0,1)$ are not computable.
Jul
25
revised Is there a number so large that we could never calculate it?
every integer is computable
Jul
25
revised Is there a number so large that we could never calculate it?
add comment about physical infeasibility
Jul
25
revised Is there a number so large that we could never calculate it?
add comment about physical infeasibility
Jul
25
revised Is there a number so large that we could never calculate it?
add comment about physical infeasibility
Jul
25
answered Is there a number so large that we could never calculate it?
Jul
24
comment Is there a number so large that we could never calculate it?
(... cont'd) See the posting math.stackexchange.com/questions/218130/… and the related WP article.
Jul
24
comment Is there a number so large that we could never calculate it?
It can be shown that in the context of ordinary mathematics (say ZFC) there are infinitely many well-specified positive integers whose decimal representations cannot be proved. E.g., for every $n \ge 10\uparrow\uparrow 10$, the Busy Beaver number $\Sigma(n)$ is well-defined and has some decimal representation $d_1d_2...d_k$, but there exists no proof that $\Sigma(n) = d_1d_2...d_k$. It isn't that the proof or the digit string is merely infeasible due to physical resource limitations; rather, such a proof is a logical impossibility.
Jul
19
comment Expected Number of Coin Tosses to Get Five Consecutive Heads
The same method obviously generalizes to give $e_n$, the expected number of tosses to get $n$ consecutive heads ($n \ge 1$): $$e_n=\frac{1}{2}(e_n+1)+\frac{1}{4}(e_n+2)+\frac{1}{8}(e_n+3)+\frac{1}{16}(e_n+‌​4)+\cdots +\frac{1}{2^n}(e_n+n)+\frac{1}{2^n}(n),$$ the solution of which is easily found to be $$e_n = 2(2^n - 1).$$
Jul
5
revised Why does this expectation integrate to 1
corrected per the posted link
Jul
5
comment Why does this expectation integrate to 1
The OP's notation involving a mysterious $\hat{y}$ makes the question almost unintelligible. The posted link makes it clear that the expectation in question is with respect to all auxiliary random variables (say $X$) used by the estimator $\hat{p}_{N}(y|\theta)$: $$\mathbb{E}_X\left[\frac{\hat{p}_{N}(y|\theta)}{p(y|\theta)}\right] = \frac{\mathbb{E}_X\left[\hat{p}_{N}(y|\theta)\right]}{p(y|\theta)} = \frac{p(y|\theta)}{p(y|\theta)} = 1.$$
Jun
27
comment How long will this take to reach.. kimye?
Yes, I think it's okay now.
Jun
27
revised How long will this take to reach.. kimye?
add inverse function
Jun
27
comment How long will this take to reach.. kimye?
I think the code is correct. E.g., I also programmed the inverse conversion and it finds 'kimye' from the input $4990767848$.