Activity for celtschk
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Edit | Post #285613 |
Post edited: Added MathJax source code as code block, and MathJax-rendering tag |
— | over 2 years ago |
| Edit | Post #285614 | Initial revision | — | over 2 years ago |
| Answer | — |
A: Why isn't MathJax table appearing? This is another instance of the general MathJax/Markdown problem noted here. If you replace all double backslashes (`\\`) with quadruple backslashes (`\\\\`), it works: $\begin{array} {|r|r|}\hline \text{If I already earned a} & \text{then I must roll another} \\\\ \hline 9 & 1 \\\\ \hline 8 & 2 ... (more) |
— | over 2 years ago |
| Suggested Edit | Post #285613 |
Suggested edit: Added MathJax source code as code block, and MathJax-rendering tag (more) |
helpful | over 2 years ago |
| Comment | Post #285596 |
The Markdown interpreter on StackExchange is sufficiently aware of MathJax syntax to avoid such things. QPixel's interpreter unfortunately isn't. The dollar sign is just one instance of that problem; also inside MathJax formulas, the backslash often needs to be doubled here.
See e.g. [here](https:... (more) |
— | over 2 years ago |
| Edit | Post #285596 | Initial revision | — | over 2 years ago |
| Answer | — |
A: Why doesn't \$ work? You need to use `\\$`, like this: \\$1. The reason is that MathJax is interpreted in the browser, while Markdown is interpreted in the server. If you write `\$`, then Markdown sees the backslash and therefore puts the dollar sign literally into the output (which it would have done anyway), with... (more) |
— | over 2 years ago |
| Edit | Post #285526 | Initial revision | — | over 2 years ago |
| Answer | — |
A: How's it possible to arrange 0 objects? How can 0! = 1? How is it possible to arrange $0$ objects? Well, by doing nothing. Doing nothing is something you can do, and you can do it in exactly one way. Another way to see it is to consider that it is also the number of ways you can rearrange the objects in a row. One way to rearrange the objects is, again... (more) |
— | over 2 years ago |
| Edit | Post #285345 | Initial revision | — | over 2 years ago |
| Answer | — |
A: Is Mathematical Induction truly "induction", or misnamed? In the context of Peano arithmetics, mathematical induction is actually an axiom, that is you cannot prove it from other properties of the natural numbers. It is extremely plausible that if something holds for $0$, and if it holds for $n$ it also holds for $n+1$, that it holds for all natural numbers... (more) |
— | over 2 years ago |
| Edit | Post #285327 | Initial revision | — | over 2 years ago |
| Answer | — |
A: Why must percent change divide the difference by the old, NOT new, value? When you say “the value changed by 5%” what you actually mean is “the value changed by 5% of the old value” (this is by convention because that is in the vast majority of cases the quantity you are interested in). And that is why you have to divide the difference by the old value. If you want to b... (more) |
— | over 2 years ago |
| Comment | Post #284788 |
Topology is a vast field. Asking whether you should learn it is like asking whether you should learn set theory. You certainly should know the fundamentals (such as, what is a neighbourhood, or what is a continuous function), and anything related to other theories you are interested in, but there's a... (more) |
— | over 2 years ago |
| Edit | Post #284557 |
Post edited: |
— | over 2 years ago |
| Edit | Post #284557 | Initial revision | — | over 2 years ago |
| Question | — |
Does this construction always give a topological vector space? Consider an algebraic vector space $V$ over $\mathbb R$ or $\mathbb C$. Now for each possible basis $Bk = \\{ei^{(k)}|i\in I\\}$ of $V$, one can define an inner product $\langle\cdot\vert\cdot\ranglek$ by $\langle ei^{(k)}\vert ej^{(k)}\ranglek = \delta{ij}$ (for vector spaces of infinite dimensio... (more) |
— | over 2 years ago |
| Comment | Post #284113 |
It is not true that for differentiating you simply “increase dot”. Rather, you apply the differentiation rules. Having said that, while taking the derivative usually can be done quite mechanically, integration cannot be done that way (well, technically it can, but the algorithm is so complicated that... (more) |
— | over 2 years ago |
| Comment | Post #283947 |
Just a note: Depending on the programming language, also in programming the subexpressions may be evaluated in any order. This is why e.g. in C and C++, expressions like `i+(i++)` are undefined behaviour. (more) |
— | over 2 years ago |
| Edit | Post #283889 | Initial revision | — | over 2 years ago |
| Answer | — |
A: Getting backward of partial differentiation's chain rule Your main error is to treat the derivatives as fractions. From the definition, they are not fractions, they are limits of fractions. Now for total derivatives treating them like fractions generally gives correct results (at least I never have seen any case where it fails), therefore one might c... (more) |
— | over 2 years ago |
| Edit | Post #283619 | Initial revision | — | over 2 years ago |
| Question | — |
MathJax doesn't render after editing comment I've just noticed that when editing a comment with MathJax, the MathJax content is not rendered after finishing the edit. Note that after a page reload, it again renders correctly. (more) |
— | over 2 years ago |
| Comment | Post #283593 |
@#53922 Yes, you understand continuous wrong. Continuity does *not* mean that the graph is path connected. Continuity means that you get arbitrary small changes of $f(x)$ for sufficiently small changes of $x$ *inside the domain.* The following would be a discontinuous function:
$$f(x) = \begin{cases... (more) |
— | over 2 years ago |
| Edit | Post #283594 | Initial revision | — | over 2 years ago |
| Answer | — |
A: What is "continuous" in Math? The terms “discrete” and “continuous” are not related to cardinality, but to topology. In particular, you can have a discrete topology on a space of arbitrary cardinality. Note also that “discrete” is a property of a set in a topological space, while “continuous” is a property of functions between... (more) |
— | over 2 years ago |
| Edit | Post #283520 | Initial revision | — | over 2 years ago |
| Answer | — |
A: Is $x=\int \int \ddot{x}\mathrm dx \mathrm dx$? While you can integrate twice for the same variable, your equation is not right. $\ddot x$ means deriving $x$ twice with respect to time, that is, $$\ddot x = \frac{\mathrm d^2x}{\mathrm dt^2}$$ which is very different from deriving twice with respect to $x$ (indeed, $\mathrm d^2x/dx^2=0$). To coun... (more) |
— | over 2 years ago |
| Edit | Post #283449 | Initial revision | — | over 2 years ago |
| Answer | — |
A: Prove that $\int \ddot{x}(t)\mathrm dt=v_0 + \frac{F_0}{m}t$ Your calculation is not correct. What you calculated is $$\\int a\\,\mathrm d\textcolor{red}{a}$$ which is something very different from $$\\int a(t)\\,\mathrm d\textcolor{red}{t}$$ Indeed, in the specific case here, $a = F0/m$ is time independent, that is, it is a constant in respect to time. No... (more) |
— | over 2 years ago |
| Comment | Post #283390 |
I personally learned GR, including the involved mathematics, from the book *Gravitation* by Misner, Thorne and Wheeler. However that's not a math book, therefore if you want mathematical rigour, that book likely isn't for you (e.g. IIRC you won't find any proofs there). Other than that I don't have s... (more) |
— | over 2 years ago |
| Comment | Post #283390 |
I haven't looked into the book (therefore only a comment), but while the topics listed in the title are relevant for quantum theory, they are generally irrelevant or at most tangentially relevant for General Relativity. Therefore I suspect that it is not the best book if your goal is to understand G... (more) |
— | over 2 years ago |
| Comment | Post #283332 |
In your perimeter example, some of the squares the circle crosses are not black; in other words, the pixels do not *cover* the circle. Otherwise you'd get a better approximation. Indeed, the Hausdorff measure is exactly defined by such coverings.
In particular, in your 1st grid, you've got 8 cover... (more) |
— | over 2 years ago |
| Comment | Post #283111 |
This isn't a question about mathematics, but about the specific language used in medicine (I'm not aware of those two terms being used outside that context). It possibly would be on-topic on a medicine site (which Codidact currently doesn't have AFAICT), but not here. It *might* me on-topic on Langua... (more) |
— | over 2 years ago |
| Edit | Post #283261 | Initial revision | — | over 2 years ago |
| Answer | — |
A: After $n - 2$ unchosen doors are opened, how does the probability of the $n - 2$ unchosen doors "shift" or "transfer" to the lone unchosen door? Maybe it's a good idea to start from a situation that's intuitive, and then gradually chance it to the Monty Hall version. So let's start with the following situation: Monty lets you choose a door. Then, after you've chosen it, he offers you to either select the chosen door, or open all the oth... (more) |
— | over 2 years ago |
| Comment | Post #283154 |
Please see the edit, I hope it clears things up. (more) |
— | over 2 years ago |
| Edit | Post #283154 |
Post edited: Fixed a typo |
— | over 2 years ago |
| Edit | Post #283154 |
Post edited: Added explannation why the area of the square is, indeed, 50 |
— | over 2 years ago |
| Comment | Post #283197 |
Yes, now I get the edit window, so that issue seems to be fixed. Thank you. (more) |
— | over 2 years ago |
| Comment | Post #283154 |
Yes, it's a square, with side length (of each of its four sides) $\sqrt{50}$. I tried to add an explanation to the answer, but at the moment for some reason I can't edit it (I've posted a bug report on meta on this). (more) |
— | over 2 years ago |
| Edit | Post #283197 | Initial revision | — | over 2 years ago |
| Question | — |
Editing my answer fails I just tried to edit this answer of mine, but for some reason clicking the edit button only reloads the page. Trying to open in a different tab didn't help either. In case it matters, I'm using Waterfox Classic 2021.02 (64-Bit) KDE Plasma Edition. (more) |
— | over 2 years ago |
| Comment | Post #283154 |
But the side length of the sketched square is not $5$, but $\sqrt{50}$. (more) |
— | over 2 years ago |
| Edit | Post #283154 | Initial revision | — | over 2 years ago |
| Answer | — |
A: How to determine area of square using Calculus in Cartesian coodinate? The correct equation for the square boundary you sketched is $$\left|x\right| + \left|y\right| = 5$$ where $\left|x\right|$ means the absolute value of $x$, that is, $$\left|x\right| = \begin{cases} x & \text{for $x\ge 0$}\\\\ -x & \text{for $x < 0$} \end{cases}$$ Now to calculate the area wi... (more) |
— | over 2 years ago |
| Edit | Post #283087 |
Post edited: Added explanation of dimensional analysis |
— | almost 3 years ago |
| Comment | Post #283087 |
Note that the fact that your result passes that test is not a proof that your result is correct, just that you cannot prove it incorrect that way (and indeed, no different power of $x$ would be correct).
On the $x$ in the numerator and denominator: You mentioned as one difference between your resu... (more) |
— | almost 3 years ago |
| Comment | Post #283087 |
Dimensional analysis is a quick check normally done on physics equations: If the equation is correct, all terms must have the correct units. Now while your equation for $I$ (probably) didn't come from a physics problem, one can pretend that it does, with $x$ having an arbitrary unit (that would depen... (more) |
— | almost 3 years ago |
| Edit | Post #283087 | Initial revision | — | almost 3 years ago |
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