Activity for r~~
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Edit | Post #284281 |
Post edited: |
— | over 2 years ago |
| Edit | Post #284281 | Initial revision | — | over 2 years ago |
| Answer | — |
A: Is Pythagorean theorem really valid in higher dimensional space? One generalization of the Pythagorean theorem to three dimensions is de Gua's theorem: > if a tetrahedron has a right-angle corner (like the corner of a cube), then the square of the area of the face opposite the right-angle corner is the sum of the squares of the areas of the other three faces ... (more) |
— | over 2 years ago |
| Edit | Post #284122 | Initial revision | — | over 2 years ago |
| Answer | — |
A: What to do when there's lot of function of time? (For integration) Should I consider them as constant? No, if you're integrating with respect to time, you can't treat functions of time as constants. Remember that, by the fundamental theorem of calculus, the result of your integration must be a function that, when differentiated, yields your original integrand. So if you incorrectly concluded that \... (more) |
— | over 2 years ago |
| Comment | Post #284051 |
There are many good questions about intuition and motivation, yes. I'm talking about a particular slim subset of those questions, where the next step in a proof is known, the reason that the step works is known, and the asker is only interested in, it would seem, the cognitive process that produced t... (more) |
— | over 2 years ago |
| Comment | Post #283900 |
@#53398, I agree that there are some ways that writing a proof is more like designing a bridge than writing a novel (and some ways that it is like neither). And yes, there are skeletons that get reused and are good to know. The sorts of questions I'm objecting to are not questions like, ‘What types o... (more) |
— | over 2 years ago |
| Comment | Post #283930 |
I'm not against (what I think is) the spirit of this answer, but I think it's out of place here. I'm not talking about questions where the asker doesn't know what the next step is; I'm talking about questions where the asker has been shown the next step, possibly understands how the step works, but w... (more) |
— | over 2 years ago |
| Edit | Post #283949 |
Post edited: |
— | over 2 years ago |
| Edit | Post #283949 | Initial revision | — | over 2 years ago |
| Answer | — |
A: What're the orders for equation expressing? Another aspect of operation precedence which Derek's otherwise excellent answer doesn't cover is operator associativity. Implicit in the PEMDAS convention is the idea that the arithmetic operators are left-associative, meaning that they should be grouped from left to right when a subexpression con... (more) |
— | over 2 years ago |
| Edit | Post #283899 |
Post edited: |
— | over 2 years ago |
| Comment | Post #283899 |
@DNB, I have given you specific feedback on each of these points on questions where they are applicable. At some point I stopped trying, since you didn't seem to be trying to incorporate the feedback into your future questions and I have better things to do with my time. But regardless, this question... (more) |
— | over 2 years ago |
| Edit | Post #283899 |
Post edited: Demote the importance of the other issues with these particular posts |
— | over 2 years ago |
| Comment | Post #283930 |
Is this an answer to the question? It seems mostly off-topic (although I might have made the question too distracting by mentioning some other problems that questions can have). (more) |
— | over 2 years ago |
| Comment | Post #283886 |
If you know both children are girls, then the information that the winter child is a girl is redundant; you know that it's a girl regardless of whether the event is described as ‘at least one winter girl’ or ‘at least one winter child’. (more) |
— | over 2 years ago |
| Edit | Post #283900 | Initial revision | — | over 2 years ago |
| Answer | — |
A: Is ‘How would you know to do the next step?’ always a bad question? I believe that yes, such questions are intrinsically bad. There are two ways to attempt to answer such a question. First, the answerer could try to get into the head of the author of the particular proof being examined, and figure out how they made the necessary leap. If the proof is well written,... (more) |
— | over 2 years ago |
| Edit | Post #283899 | Initial revision | — | over 2 years ago |
| Question | — |
Is ‘How would you know to do the next step?’ always a bad question? We have a user who keeps posting questions of the form, ‘How would you [tortured synonym for “know”] to [do the next step in a proof]?’ Leaving aside the various other reasons that these posts are bad^[I don't want those other issues to be a distraction from the central question here. I'm only mentio... (more) |
— | over 2 years ago |
| Edit | Post #283877 | Initial revision | — | over 2 years ago |
| Answer | — |
A: Getting backward of partial differentiation's chain rule The difference between a partial derivative and a total derivative is that the partial derivative measures the change in a function when only one of its arguments varies, while the total derivative measures the change in a function when all of its arguments vary. The $\frac{\partial z}{\partial x}$ n... (more) |
— | over 2 years ago |
| Edit | Post #283707 |
Post edited: |
— | over 2 years ago |
| Edit | Post #283707 | Initial revision | — | over 2 years ago |
| Answer | — |
A: Find limits of integration in polar coordinates Regardless of the coordinate system, the principle of finding the limits of integration is the same: find the minimum and maximum value of the independent coordinate that enclose the region of interest. In polar coordinates, for these two particular curves, the region of interest is best described... (more) |
— | over 2 years ago |
| Comment | Post #283593 |
$f(x) = \frac{1}{x-1}$ is considered continuous. It's not defined at $x = 1$, so it has a disconnected domain, but it is continuous at all values where it is defined. (more) |
— | over 2 years ago |
| Comment | Post #283385 |
This is not a question about math. (more) |
— | over 2 years ago |
| Edit | Post #283173 | Initial revision | — | over 2 years ago |
| Answer | — |
A: How can "information about the birth season" bring "at least one is a girl" closer to "a specific one is a girl"? ‘More specific information’, here, is informally referring to the value of the (positive) likelihood ratio: the ratio between how likely it is to get that information if a proposition is true, and how likely it is to get that information if the proposition is false. (I say ‘informally’ because, as yo... (more) |
— | over 2 years ago |
| Edit | Post #282600 |
Post edited: |
— | almost 3 years ago |
| Comment | Post #282615 |
Nope. As written, this is a complete answer to your original question. You asked a new question here in the comments. (more) |
— | almost 3 years ago |
| Comment | Post #282892 |
Have you tried to understand why? Take some example values of $s$, $c$, and $n$, and see what happens to the value of that fraction as $n$ increases. (more) |
— | almost 3 years ago |
| Edit | Post #282892 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: How does $\lim\limits_{n \to \infty} \dfrac{p[s + (1 - s)c^n]}{p[ s + (1 - s)c^n] + (1 - p)[s + (1 - s)w^n]} = p?$ > So if $n \to \infty$, then all terms above containing $c^n \to 0$. This is false. It's true that as $n \to \infty$, $c^n \to 0$ (for $0 < c < 1$). But a term like $\frac{s}{c^n}$ will diverge instead of converging to $0$. You haven't done yourself any favors by dividing everything by $c^n$... (more) |
— | almost 3 years ago |
| Comment | Post #282615 |
An algebraic expression is made exclusively of numbers, variables, and algebraic operations. $\ldots$ is none of these. This really isn't any more complicated than that. Doing algebra with informal notations can get you into trouble if you don't keep in mind what the informal notations mean. This is ... (more) |
— | almost 3 years ago |
| Comment | Post #282873 |
You moved your coloring back one paragraph. Look at the paragraph that is now above your red phrase. That is the explanation. And you need to explain why you think 2 and 3 are true; I can't read your mind. (more) |
— | almost 3 years ago |
| Comment | Post #282873 |
The answer to 1 was given just two paragraphs earlier. 2 and 3 are not true and not implied by anything in the solution. (more) |
— | almost 3 years ago |
| Edit | Post #282780 |
Post edited: Think you missed a term in your last equation |
— | almost 3 years ago |
| Suggested Edit | Post #282780 |
Suggested edit: Think you missed a term in your last equation (more) |
helpful | almost 3 years ago |
| Comment | Post #282737 |
Is this a homework assignment? What have you tried? Where are you stuck? We can help but we aren't going to do the assignment for you. (more) |
— | almost 3 years ago |
| Edit | Post #282712 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: How to derive some trigonometric formulas? Can't use algebra, you say? Nonsense! All you need is Euler's formula $$ e^{i\theta} = \cos\theta + i\sin\theta $$ and these identities just fall out of the algebra. For example: \begin{align} \sin (\alpha + \beta) &= \frac1{2i} \left(e^{i(\alpha + \beta)} - e^{-i(\alpha + \beta)}\right)\\\\ ... (more) |
— | almost 3 years ago |
| Edit | Post #282665 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: $\sum_{k=0}^{n} \binom{n}{k}=2^{n} \overset{?}{\iff} \sum_{k=0}^{n} \binom{2n+1}{k}=2^{2n}$ The green result can be used to prove the red one, yes. Start with the fact that $\binom{m}{k} = \binom{m}{m - k}$. If this isn't obvious to you, you can derive it either by looking at the usual formula for the binomial, or by considering that choosing the members of a subset is equivalent to choo... (more) |
— | almost 3 years ago |
| Edit | Post #282654 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: How does the change of variable $\color{red}{r↦n−r}$ transmogrify $\sum\limits_{r=0}^n2^{n-r}\binom{n+r}{n}=2^{2n}$ into $\sum\limits_{k=0}^{n} \frac{\binom{2n-k}{n}}{2^{2n-k}}=1$? $n$ is free in the expression $\sum{r=0}^n 2^{n-r}\binom{n+r}{n}$. The only variable not free in that expression is $r$. What $\sum{r=0}^n$ means is to treat what comes next as a function of $r$, and compute the sum of that function evaluated at $0$, $1$, and so on up to $n$. If $n$ is used inside th... (more) |
— | almost 3 years ago |
| Comment | Post #282652 |
The variance argument is only relevant if you draw from the same urn multiple times, which isn't part of the original problem. With one draw, the author is correct that you should be indifferent. Your argument is interesting additional information, but I think it's misleading to present it as a count... (more) |
— | almost 3 years ago |
| Edit | Post #282638 |
Post edited: |
— | almost 3 years ago |
| Edit | Post #282638 |
Post edited: |
— | almost 3 years ago |
| Edit | Post #282638 |
Post edited: |
— | almost 3 years ago |