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Activity for Groveā€­

Type On... Excerpt Status Date
Comment Post #290318 So as I suspected my claim was (technically) wrong, but because most numbers are normal, not (as I thought) because most numbers aren't.
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7 months ago
Edit Post #290318 Initial revision 7 months ago
Question Is it known whether most numbers are normal or not
In a comment over at mathematics.stackexchange.com, I just (well, now stuff has happened and it's 8 hours ago) claimed that for most numbers it is not known whether they are normal. And then I got to think whether that is actually true? Is there some set of numbers that (in some way, whether my me...
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7 months ago
Edit Post #286961 Post edited:
Chnaged formatting
almost 2 years ago
Edit Post #286961 Post edited:
Described that you can add a constant to the functions solving the orgonal problem
almost 2 years ago
Comment Post #286961 I don't think negative values for $k$ or $j$ produces any functions that are really different from what we get if we choose $y$ properly, ($-\sin(x)=\sin(-x)=\sin(x+\pi)$), so having a lower bound of $0$ on them makes sense. The upper bound on $k$ is to make sure $f$ stays below $1$, the upper bound ...
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almost 2 years ago
Comment Post #286961 Oops. That was just a typo here (I made it consistently though), the hand-written notes I had on this, actually said $[-1,1]$. When I fixed that, I realised that $k$ can also range down to $-1$, and $j$ can also be negative, but to what degree do I get new functions, and to what degree is it just fun...
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almost 2 years ago
Edit Post #286961 Post edited:
almost 2 years ago
Edit Post #286961 Initial revision almost 2 years ago
Question Is $f(x)=\sin(x)$ the unique function satisfying $f'(0)=1$ and $f^{(n)}(\Bbb R)\subset [-1,1]$ for all $n=0,1,\ldots$?
> Question. Is there a function $f:\Bbb R \to \Bbb R$ with $f'(0)=1$ and $f^{(n)}(x)\in [-1,1]$ for all $n=0,1,\ldots$ and $x\in \Bbb R$, other than $f(x)=\sin(x)$? Going through some old notes, I stumbled upon this question, I don't remember where it take from/what inspired me to look at it. If t...
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almost 2 years ago
Edit Post #283591 Initial revision almost 3 years ago
Answer A: What is "continuous" in Math?
There are more possible cardinalities above the the Cardinality of the continuum which is $2^{\aleph0}$ (e.g. $2^{2^{\aleph0}}$ - that wikipedia page even mentions this, have you actually read that), sets of those sizes generally don't contain discrete things, so your distinction is simply wrong, but...
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almost 3 years ago
Comment Post #282642 Technically $\Leftrightarrow$ just means that the statements on either side have the same truth value. As both are true, the statement in your title is true. But as "$2=2$" and $\text{FLT}$ (Fermat's last theorem) are both true, we can also write $2=2 \Leftrightarrow \text{FLT}$, but that doesn't rea...
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almost 3 years ago
Edit Post #278332 Post edited:
over 3 years ago
Edit Post #280373 Post edited:
over 3 years ago
Edit Post #280373 Post edited:
over 3 years ago
Edit Post #280373 Initial revision over 3 years ago
Answer A: Are 3 10% chances better than one 30% chance (when penalized by a variable for failures)?
As you seem to know (the $10\times 10\\% \neq 100\\%$-stuff - but continue doing anyway) and celtschk's answer shows you can't add the probabilities like that. (The events aren't independent) The expected number of upgrades are the same, but what you really need to weigh against each other is the ...
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over 3 years ago
Edit Post #280348 Initial revision over 3 years ago
Question Normal in one base and not in another?
Examples of numbers that are normal in some bases are known (Champernowne's $0.12345678910111213\ldots$ is probably the most well-known example of a number that is normal in base 10). To my knowledge (but please correct me if I'm wrong) no numbers that are normal (in all bases) are known. But a...
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over 3 years ago
Edit Post #278332 Post edited:
over 3 years ago
Edit Post #278332 Post edited:
over 3 years ago
Comment Post #278332 No. $B_1$ does not have area $1/1$, $n$ is fixed throughout the procedure so all the $B_k$'s have area $1/n$., and I thought that was conveyed by using $k$ as index on the $B$'s when defining those. (And of course it's a mistake that I forgot an index on that $S$, I will add it right after posting th...
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over 3 years ago
Edit Post #278332 Post edited:
over 3 years ago
Edit Post #278332 Post edited:
over 3 years ago
Edit Post #278332 Initial revision over 3 years ago
Question Cutting the square
I don't know how simple/diffcult this is, but it has been on my mind for some time, and I haven't managed to do anything about it, so now I'll try here to see if anyone has any input. Let a natural number $n\in\mathbb N$ be given. Start with a square $S0$ with sidelength $1$. For $k$ in $\\{...
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over 3 years ago