Activity for celtschk
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Answer | — |
A: differentiate under integral sign says something went wrong Assuming you copied the formula from the book correctly, your mistake is simply to assume that your book is right. As a physicist, my first instinct was to make a dimensional analysis. The formula for $I$ gives a dimensionally valid expression as long as $a$ and $b$ have the inverse unit of $x$ (s... (more) |
— | almost 3 years ago |
| Edit | Post #282975 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: What's wrong with evaluating $n(n-1) \dots (n-[k-3])(n-[k-2])\color{red}{(n-[k-1])}$ at $k = 1$? The informal expression stands for the formal expression $$\prod{j=1}^k (n-j+1)$$ where, since it is a formal expression, you indeed can insert $k=1$, to get $$\prod{j=1}^1 (n-j+1) = (n-1+1) = n$$ as the text states. Now the author of the text obviously wanted to avoid the product notation, ei... (more) |
— | almost 3 years ago |
| Edit | Post #282652 |
Post edited: Another interference |
— | almost 3 years ago |
| Edit | Post #282652 |
Post edited: Fixed markdown interferring with MathJax |
— | almost 3 years ago |
| Edit | Post #282652 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: Why rational to be indifferent between two urns, when urn A has 50-50 red and white balls, but you don't know urn B's ratio? Let's assume you know that urn B has 5 balls in it. I deliberately take an odd number, because that way we know for sure that there are not exactly the same number of red and white balls in that urn. Note that since you don't know the content of the urn, you have to assign probabilities to the urn... (more) |
— | almost 3 years ago |
| Comment | Post #282343 |
Unless I've missed something, all MathJax I could see on the page (including that in comments) renders fine for me (Waterfox Classic/Linux). (more) |
— | almost 3 years ago |
| Comment | Post #281203 |
Thank you for your answer (and sorry for my late reaction). Indeed I was after the space spanned by finite linear combinations of the $\omega_i$; I thought (incorrectly, as I now see) that I had found a base-independent characterisation, which would have meant that it is base independent. So IIUC, th... (more) |
— | almost 3 years ago |
| Edit | Post #281016 | Initial revision | — | about 3 years ago |
| Answer | — |
A: Intuitively, why's X% of Y = Y% of X? Just consider that Z is Z percent of 100. Then you get: > X percent of Y is X percent of Y percent of 100, which is Y percent of X percent of 100, which is Y percent of X. I think that X percent of Y percent of something is the same as Y percent of X percent of something is intuitive. And that ... (more) |
— | about 3 years ago |
| Edit | Post #281014 | Initial revision | — | about 3 years ago |
| Answer | — |
A: In "if and only if" proofs, why's 1 direction easier to prove than the other? One thing to consider is that the equivalences are generally based on the validity of certain axioms. And then, one direction may only depend on a smaller set of axioms. Now it is possible that the additional axioms help also in the direction that doesn't need it, but it is also possible that the ea... (more) |
— | about 3 years ago |
| Edit | Post #281011 | Initial revision | — | about 3 years ago |
| Answer | — |
A: Why aren't $z_1=f(xy)$ and $z_2=f(x/y)$ functions of 2 variables? You are misrepresenting what Hagen von Eitzen wrote. He did not write that $z1$ and $z2$ depend on only one variable. He wrote that $f$ is a function of only one variable. That's a massive difference. The question this refers to was whether $z1=f'(xy)$ or $z2=f'(x/y)$ are ambiguous, and the correc... (more) |
— | about 3 years ago |
| Edit | Post #280800 | Initial revision | — | about 3 years ago |
| Answer | — |
A: Why should a non-commutative operation even be called "multiplication"? In most (but not all) cases where you name an operation multiplication is when you have two binary operations, and one of them distributes over the other, but not the other way round. Then the operation that distributes over the other is called multiplication and the other one addition, in analogy to... (more) |
— | about 3 years ago |
| Edit | Post #280799 | Initial revision | — | about 3 years ago |
| Question | — |
Is this topology basis dependent? Consider a topological field $K$ and an algebraic(!) vector space $V$ over $K$, that is, $V$ has not (yet) a topology defined on it. I'm particularly interested in the case where $V$ has infinite dimension. Now be $V^\ast$ the algebraic dual of $V$. Define a topology on $V^\ast$ through pointwise ... (more) |
— | about 3 years ago |
| Comment | Post #280654 |
Thank you. I did know the term embedding for Riemannian manifolds, but wasn't aware of the purely topological usage. Stated that way, the relation looks natural enough that someone ought to have thought of it before. (more) |
— | about 3 years ago |
| Edit | Post #280572 |
Post edited: Fixed a typo |
— | over 3 years ago |
| Edit | Post #280572 | Initial revision | — | over 3 years ago |
| Question | — |
Does this generalization of path-connectedness also cover general connectedness? I've got the following idea to generalise path-connectedness: Given a topological space $P$ and a subspace $S$, a space $X$ is $(P,S)$-connected if every continuous function $f:S\to X$ can be extended to a continuous function $g:P\to X$. The usual path-connectedness is obtained using $P=[0,1]$ ... (more) |
— | over 3 years ago |
| Edit | Post #280524 |
Post edited: Fixed a typo |
— | over 3 years ago |
| Edit | Post #280524 | Initial revision | — | over 3 years ago |
| Question | — |
Are there useful topologies on Cartesian products “in between” the product topology and the box topology? On the Cartesian product of topological spaces, there are two standard topologies: One is the product topology, the other is the box topology. As is well known, the box topology is generated by the product of open sets, and the product topology is generated by such products with the restriction th... (more) |
— | over 3 years ago |
| Comment | Post #280340 |
Maybe it would be a good idea to make the autosave interval configurable (ideally per community, or simply two settings depending on whether MathJax is enabled or disabled). An autosave every five minutes would still be quite useful, but probably not too disruptive even with MathJax rendering. (more) |
— | over 3 years ago |
| Comment | Post #280462 |
I think in the presence of a crosscap, each handle should be convertible to two crosscaps, therefore $g$ handles and $k$ crosscaps with $k\ge 1$ should be equivalent to $2g+k$ crosscaps. But I'm not entirely sure. (more) |
— | over 3 years ago |
| Edit | Post #280313 | Initial revision | — | over 3 years ago |
| Answer | — |
A: Are 3 10% chances better than one 30% chance (when penalized by a variable for failures)? It somewhat depends on your game situation. If you have just that one weapon, need to upgrade it urgently, and are likely to have enough coins the next time you need to upgrade a weapon, then clearly the 30% option is better: It gives you a 30% probability of upgrade, while three 10% attempts give... (more) |
— | over 3 years ago |
| Comment | Post #280068 |
@tommi: One case where the $1/\sqrt{3}$ definitely is more useful is as coefficient in a quantum state: You see immediately that the absolute square (which gives the corresponding probability) is $1/3$, which for $\sqrt{3}/3$ takes more cognitive load to see. Therefore which convention is more useful... (more) |
— | over 3 years ago |
| Comment | Post #280134 |
On the duplication issue: Maybe one could make a FAQ category populated with curated answers to popular questions. The FAQ would initially be populated by questions crafted on frequent questions on Math SE, and later extended to cover questions that turn out to be asked frequently here. This could be... (more) |
— | over 3 years ago |
| Comment | Post #280133 |
I think the first thing that has to be addressed is the bad interaction between MarkDown and MathJax on this site (the backslash problem). See [here](https://math.codidact.com/posts/278763) for details. I have some ideas on how this might be addressed on an algorithmic level, but unfortunately I have... (more) |
— | over 3 years ago |
| Comment | Post #280127 |
@luap42: Thank you; you're quick! (more) |
— | over 3 years ago |
| Edit | Post #280127 | Initial revision | — | over 3 years ago |
| Question | — |
Inconsistency of answer count between main page and question page The question “Cutting the square” is listed on the main page as having one answer, however when going to that question, it says 0 answers (and indeed, no answer is shown). Something doesn't add up here. [1]: https://math.codidact.com/posts/278332 (more) |
— | over 3 years ago |
| Comment | Post #280068 |
@tommy: That assumes that the numerical value is what you are interested in. Which is sometimes the case, but certainly not always. (more) |
— | over 3 years ago |
| Comment | Post #280069 |
Note that your third "we want" point is a direct consequence of the first two. Anyway, great answer, +1. (more) |
— | over 3 years ago |
| Comment | Post #279400 |
I have trouble to figure out what your intuition actually is. What is the unit of the denominator $2$ in "half a cake"? Anyway, the $1$ has to be dimensionless (having no unit) for the formula to work. It just means the number one. (more) |
— | over 3 years ago |
| Edit | Post #279117 | Initial revision | — | over 3 years ago |
| Question | — |
$sitename not substituted in FAQ In the FAQ there appears the term "$sitename" several times. I'm pretty sure that's the name of a variable that should have been substituted here. (more) |
— | over 3 years ago |
| Edit | Post #279048 | Initial revision | — | over 3 years ago |
| Answer | — |
A: Why does “unless” mean “if not”? According to the definition you quote, “unless” gives an exception to a preceding negative statement. An exception to a statement is a condition in which the statement does not apply. Therefore the statement does apply only if the condition is not fulfilled (because otherwise the exception applies, a... (more) |
— | over 3 years ago |
| Comment | Post #279026 |
@msh: I've now looked up the small inductive dimension, and I don't think it fits. In particular, the point types in general are only partially ordered, while the small inductive dimensions are by construction totally ordered. Also, if you equip a von-Neumann ordinal $\alpha$ with the topology $\alph... (more) |
— | over 3 years ago |
| Edit | Post #279036 | Initial revision | — | over 3 years ago |
| Answer | — |
A: Why does the decimal expansion of $1/(10n - 1)$ have this neat pattern? I think the simplest way to see how it works is as follows: Given $x=\frac{1}{10n-1}$, it is easy to check that $\frac{x+1}{10}=nx$. Now $\frac{x+1}{10}$ means shifting the digits to the right, with an $1$ added as the first decimal. For example, in the case of $x=1/19$, we have $$\frac{x+1}{1... (more) |
— | over 3 years ago |
| Comment | Post #278772 |
One possibility to fix this is before passing it to MarkDown to pass it through another code which escapes all backslashes occurring inside MathJax expressions. That code would only have to detect the configured MathJax triggers (i.e. the dollar signs, and whatever else MathJax is configured to inter... (more) |
— | over 3 years ago |
| Comment | Post #278724 |
Happens also for me with Waterfox Classic on Linux. In particular the re-rendering on moving the cursor is annoying; a re-rendering should only be triggered when the edited content actually changes. (more) |
— | over 3 years ago |
| Comment | Post #278332 |
OK, so $S_0$ is a unit square. $B_1$ is a section of $S_0$ of area $1/1$, that is, all of $S_0$ except for a null set. Since it is a section by a straight line, that null set can be either empty, a corner point or a side. $S_1 = S_0\setminus B_1$ (your $S$ at that point misses an index, but up to now... (more) |
— | over 3 years ago |
| Edit | Post #279026 |
Post edited: Fixed a wrong word |
— | over 3 years ago |
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