https://pop.com.sgExplosive pop stories with broad entertainment appeal.en-usMon, 07 Sep 2026 14:51:14 -0400https://pop.com.sg/drawing-direction-fields-online.htmlhttps://pop.com.sg/drawing-direction-fields-online.htmlI am looking for a convenient and free online tool for plotting Direction Fields and Solution Curves of Ordinary Differential Equations. I tried the "Slope Field Plotter" on Geogebra; it worked tol......Mon, 07 Sep 2026 18:47:57 -0400https://pop.com.sg/multiplying-a-matrix-by-a-row-vector.htmlhttps://pop.com.sg/multiplying-a-matrix-by-a-row-vector.htmlIs multiplying a matrix by a row vector the same as multiplying it by a column vector? Or are there any differences between the two?...Mon, 07 Sep 2026 18:46:28 -0400https://pop.com.sg/how-do-you-jungle-in-smite.htmlhttps://pop.com.sg/how-do-you-jungle-in-smite.htmlI'm not very familiar with jungling in Smite. Assuming that you've picked an appropriate jungler, what does the jungler do during the course of the game? Some information I'm looking for is: Star......Mon, 07 Sep 2026 18:33:10 -0400https://pop.com.sg/solving-lyapunov-equation-matlab-has-different-solution-why.htmlhttps://pop.com.sg/solving-lyapunov-equation-matlab-has-different-solution-why.htmlI need to solve the lyapunov equation i.e. $A^TP + PA = -Q$. With $A = \begin{bmatrix} -2 & 1 \\ -1 & 0 \end{bmatrix}$ and $Q = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}$. Hence.......Mon, 07 Sep 2026 18:23:01 -0400https://pop.com.sg/how-do-i-read-strawberry-facts.htmlhttps://pop.com.sg/how-do-i-read-strawberry-facts.htmlIn Fruit Ninja, to unlock one of the achievements, you have to "Read three strawberry facts". What does that mean? Somehow, I got that achievement; how did I do it?...Mon, 07 Sep 2026 18:10:35 -0400https://pop.com.sg/getting-the-sequence-1-0-1-0-1-0-1-0-ldots-without-trig.htmlhttps://pop.com.sg/getting-the-sequence-1-0-1-0-1-0-1-0-ldots-without-trig.htmlWhat's the simplest way to write a function that outputs the sequence: {1, 0, -1, 0, 1, 0, -1, 0, ...} ... without using any trig functions? I was able to come up with a very complex sequence ...Mon, 07 Sep 2026 17:58:55 -0400https://pop.com.sg/the-two-definitions-of-a-compact-set.htmlhttps://pop.com.sg/the-two-definitions-of-a-compact-set.htmlIn general, $A$ is compact if every open cover of $A$ contains a finite subcover of $A$. In $R$, $A$ is compact if it is closed and bounded. The second is very easy to understand because I can ea......Mon, 07 Sep 2026 17:51:45 -0400https://pop.com.sg/what-should-the-width-of-the-border-be-closed.htmlhttps://pop.com.sg/what-should-the-width-of-the-border-be-closed.htmlYou have made a rectangular stained glass window that is $2$ feet by $4$ feet. You have 7 square feet of clear glass to create a border of uniform width around the window. What should the width of ......Mon, 07 Sep 2026 17:49:44 -0400https://pop.com.sg/find-the-function-arcsin-cos-x.htmlhttps://pop.com.sg/find-the-function-arcsin-cos-x.htmlQuestion is from Spivak's Calculus 15-18. It asks to find the function $\arcsin(\cos x)$. Answer below: I have problem with the highlighted part. If that is true, then why is it our answer for ......Mon, 07 Sep 2026 17:48:29 -0400https://pop.com.sg/how-do-the-new-missions-work-in-cs-go.htmlhttps://pop.com.sg/how-do-the-new-missions-work-in-cs-go.htmlWith the latest Patch and Operation Breakthrough Valve has introduced Missions to the game. As far as I can see you get 2 objectives with 1 Mission. My question is, do the missions cycle over tim......Mon, 07 Sep 2026 17:45:15 -0400https://pop.com.sg/derivative-of-the-2-norm-of-a-multivariate-function.htmlhttps://pop.com.sg/derivative-of-the-2-norm-of-a-multivariate-function.htmlI've got a function $$g(x,y) = \| f(x,y) \|_2$$ and I want to calculate its derivatives with respect to $x$ and $y$. Using Mathematica, differentiating w.r.t. $x$ gives me $ f'_x(x,y) \text{Norm}'(......Mon, 07 Sep 2026 17:42:02 -0400https://pop.com.sg/eigenvalues-of-tensor-product-of-matrices-question-about-general-prope.htmlhttps://pop.com.sg/eigenvalues-of-tensor-product-of-matrices-question-about-general-prope.htmlI would like to refresh my mind on eigenvalues/eigenvector of tensor product of operator (for Quantum Mechanics purposes). Consider two hermitic matrices $A$ and $B$ living in Hilbert spaces of fi......Mon, 07 Sep 2026 17:32:04 -0400https://pop.com.sg/find-the-point-normal-form-for-this-line-passing-through-point-p.htmlhttps://pop.com.sg/find-the-point-normal-form-for-this-line-passing-through-point-p.htmlGive the point-normal form for the following 2D line with the following description: - Through P(-2,5) and perpendicular to the line x + 2y = 5 I know that the point-normal form is n * (x - p) = 0......Mon, 07 Sep 2026 17:12:18 -0400https://pop.com.sg/what-does-the-notation-0-1-mean.htmlhttps://pop.com.sg/what-does-the-notation-0-1-mean.htmlI am studying the procedure for bucket sort from Introduction To Algorithms by Cormen et al, which assumes that the input is generated by a random process that distributes the elements uniformly and ...Mon, 07 Sep 2026 17:03:22 -0400https://pop.com.sg/skyrim-potions-for-boosting-alchemy-skill.htmlhttps://pop.com.sg/skyrim-potions-for-boosting-alchemy-skill.htmlI'd like to know what ingredients (if any) will make a potion of fortify alchemy in skyrim...Mon, 07 Sep 2026 17:00:50 -0400https://pop.com.sg/how-to-befriend-a-dog.htmlhttps://pop.com.sg/how-to-befriend-a-dog.htmlA loading screen tip told me that by befriending a dog, it could show me some interesting things. How do I do that? If I shove myself into the dog for a while, hearts will show up, be it will stay ...Mon, 07 Sep 2026 17:00:32 -0400https://pop.com.sg/how-can-i-gain-curie-039-s-approval-quickly.htmlhttps://pop.com.sg/how-can-i-gain-curie-039-s-approval-quickly.htmlI went with Nick Valentine as companion for most of the time, but now that I completed his quest I switched to Curie. Valentine was easy to please, but I'm having a much harder time rising Curie's ...Mon, 07 Sep 2026 16:55:23 -0400https://pop.com.sg/how-do-you-apply-potion-effects-to-players.htmlhttps://pop.com.sg/how-do-you-apply-potion-effects-to-players.htmlI'm developing a minigame server. I just need to know what commands to use, via command block, to give players special effects infinitely such as: speed boost, regeneration, or jump boost. I know i......Mon, 07 Sep 2026 16:48:29 -0400https://pop.com.sg/does-rainbow-six-siege-lag-a-lot-if-you-play-on-windows-via-virtualbox.htmlhttps://pop.com.sg/does-rainbow-six-siege-lag-a-lot-if-you-play-on-windows-via-virtualbox.htmlI'm curious to know as I have a Mac and I want to play Rainbow Six Siege via VirtualBox but I don't want it to be a waste if it lags too much....Mon, 07 Sep 2026 16:46:10 -0400https://pop.com.sg/how-do-i-hook-up-my-gamecube-to-my-desktop.htmlhttps://pop.com.sg/how-do-i-hook-up-my-gamecube-to-my-desktop.htmlSo I bought an PC/LAPTOP VGA SVGA TO S-Video 3 RCA Composite AV TV Out Converter Adapter Cable to play my GameCube on my Monitor but I can figure out how to Switch it? This is where I got the Cable......Mon, 07 Sep 2026 16:41:45 -0400https://pop.com.sg/integral-of-e-x-3-x-2-1-3x-4-2x-3-2x.htmlhttps://pop.com.sg/integral-of-e-x-3-x-2-1-3x-4-2x-3-2x.htmlI understand that this looks exactly like a "Do my Homework" kinda question but trust me, I've spent hours(I won't go into detail as it's off topic). Note: I'm a High School student, our teacher gave ...Mon, 07 Sep 2026 16:41:39 -0400https://pop.com.sg/greatest-number-of-regions-we-can-get-when-dividing-with-lines-and-cir.htmlhttps://pop.com.sg/greatest-number-of-regions-we-can-get-when-dividing-with-lines-and-cir.htmlWhat is the greatest number of regions a plane can be divided into using $n$ straight lines? What about $n$ circles? Can you generalize this into 3-dimensional space, planes and spheres? For line......Mon, 07 Sep 2026 16:38:08 -0400https://pop.com.sg/how-do-i-reset-npcs-in-skyrim.htmlhttps://pop.com.sg/how-do-i-reset-npcs-in-skyrim.htmlI have been trying to play the Mage's College quest, but Mirabelle Ervine is frozen in place and can't go anywhere. I can still talk to her, but that's about all I can do. How can I reset her or re......Mon, 07 Sep 2026 16:23:56 -0400https://pop.com.sg/how-many-bit-strings-of-length-5-do-not-have-consecutive-1-039-s.htmlhttps://pop.com.sg/how-many-bit-strings-of-length-5-do-not-have-consecutive-1-039-s.htmlHow many bit strings of length 5 do not have consecutive 1's? I'm trying to think of a way to calculate how many ways we can arrange a string of length 5 starting with the first position (or index......Mon, 07 Sep 2026 16:05:51 -0400https://pop.com.sg/what-counters-ap-kog-039-maw-in-mid.htmlhttps://pop.com.sg/what-counters-ap-kog-039-maw-in-mid.htmlI played a few games over the weekend and I kept seeing a bunch of AP Kog'maw players and they were giving me a really hard time in mid. What are some solid counter picks or strategies I could use ...Mon, 07 Sep 2026 16:04:18 -0400https://pop.com.sg/how-is-the-damage-for-reverse-slash-calculated.htmlhttps://pop.com.sg/how-is-the-damage-for-reverse-slash-calculated.htmlI have a question regarding ESO skill reverse slash. In the skill description it says: "Gives up to 300% more damage against enemies under 50%". The thing is, how is that up to computed? Is it ran......Mon, 07 Sep 2026 16:02:37 -0400https://pop.com.sg/lim-sup-and-lim-inf-of-sequence-of-sets.htmlhttps://pop.com.sg/lim-sup-and-lim-inf-of-sequence-of-sets.htmlI was wondering if someone would be so kind to provide a very simple explanation of lim sup and lim inf of s sequence of sets. For a sequence of subsets $A_n$ of a set $X$, the $\limsup A_n= \bigc......Mon, 07 Sep 2026 15:59:48 -0400https://pop.com.sg/what-is-the-complexity-of-complex-matrix-multiplication-closed.htmlhttps://pop.com.sg/what-is-the-complexity-of-complex-matrix-multiplication-closed.htmlI want to calculate the complexity of an algorithm in MATLAB (not the time complexity), however, all the matrices are complex ones. I guess that the complexity of complex matrix multiplication is h......Mon, 07 Sep 2026 15:42:37 -0400https://pop.com.sg/why-particular-integral-gives-two-different-values-in-two-different-me.htmlhttps://pop.com.sg/why-particular-integral-gives-two-different-values-in-two-different-me.htmlI would like to find out the particular integral (P.I.) of the differential equation : $$(D^2-5D+6)y=e^{2x}$$ Result: P.I. of the D.E., $F(D)y=X$ is (i) $\dfrac{1}{F(D)}e^{ax}=\dfrac{1}{F(a)}e^{a......Mon, 07 Sep 2026 15:37:06 -0400https://pop.com.sg/lost-all-buddies-in-metal-gear-solid-v.htmlhttps://pop.com.sg/lost-all-buddies-in-metal-gear-solid-v.htmlI am going through all of the side ops in MGSV and on one of the ops eliminating a tank unit Quiet took a lot of fire and was extracted. Now I have no buddies at all available for missions. How do......Mon, 07 Sep 2026 15:35:22 -0400https://pop.com.sg/finding-coefficients-of-legendre-polynomials.htmlhttps://pop.com.sg/finding-coefficients-of-legendre-polynomials.htmlBy considering the 2-norm(least squares) approximation of $f(x)=e^x$ for $-1\le x\le 1$ by a polynomial of degree $N$ which is expanded into a series of Legendre polynomials $P_j(x):$ $$Q_N(x)=\su......Mon, 07 Sep 2026 15:34:39 -0400https://pop.com.sg/how-to-use-custom-names-and-lores-in-minecraft-1-14-2-duplicate.htmlhttps://pop.com.sg/how-to-use-custom-names-and-lores-in-minecraft-1-14-2-duplicate.htmlHow can I give myself an item with a custom name, and how can I search for a player holding an item with a certain name. This is what I tried: /give @p minecraft:acacia_button{display:{Name:"ieat",...Mon, 07 Sep 2026 15:25:10 -0400https://pop.com.sg/where-can-i-find-a-new-place-to-live.htmlhttps://pop.com.sg/where-can-i-find-a-new-place-to-live.htmlWhen I first, let's say arrived, in Fallen London, real estate opportunities were scarce for someone of my... standing. I certainly wasn't too choosy back then, but now that I feel a little more s......Mon, 07 Sep 2026 15:21:39 -0400https://pop.com.sg/solutions-of-sixth-order-polynomial-equations.htmlhttps://pop.com.sg/solutions-of-sixth-order-polynomial-equations.htmlDo you know a way to solve exactly a general sixth order polynomial equation: $x^{6}+a_{5}x^{5}+a_{4}x^{4}+a_{3}x^{3}+a_{2}x^{2}+a_{1}x+a_{0}=0$ ? According to this link, it is possible to solve ......Mon, 07 Sep 2026 15:11:34 -0400https://pop.com.sg/solution-verification-exercise-1-4-in-brezis-039-s-functional-analysis.htmlhttps://pop.com.sg/solution-verification-exercise-1-4-in-brezis-039-s-functional-analysis.htmlExercise 1.4 in Brezis's Functional Analysis, Sobolev Spaces and partial Differential Equations reads as follows: Let $E = c_0$ be the space of real sequences tending to $0$ with norm $||u|| = \......Mon, 07 Sep 2026 15:07:07 -0400https://pop.com.sg/what-does-r-rightarrow-r-means-in-functions.htmlhttps://pop.com.sg/what-does-r-rightarrow-r-means-in-functions.htmlI have a function. The function is: $$ f:R \rightarrow R $$ $$ f(x) = x^3$$ What does $R \rightarrow R$ means? I don't know what types of questions should I ask here. If it is not ok, the I will ...Mon, 07 Sep 2026 15:03:30 -0400https://pop.com.sg/what-is-the-purpose-of-those-friendly-big-plant-looking-creatures.htmlhttps://pop.com.sg/what-is-the-purpose-of-those-friendly-big-plant-looking-creatures.htmlNot sure how best to describe them. There is a big momma type one and 2-3 baby ones. They look like big fat plants and they have a creepy love towards me. If you hit them they say something like "o......Mon, 07 Sep 2026 15:02:50 -0400https://pop.com.sg/learning-arcsin-arccos-arctan-how-to.htmlhttps://pop.com.sg/learning-arcsin-arccos-arctan-how-to.htmlSorry for asking such question. I have a very basic understanding of $\arcsin, \arccos, \arctan$ functions. I do know how their graph looks like and not much more beyond that. Calculate: Which ...Mon, 07 Sep 2026 14:47:08 -0400https://pop.com.sg/is-it-possible-to-sell-stolen-items.htmlhttps://pop.com.sg/is-it-possible-to-sell-stolen-items.htmlI recently discovered the average shopkeeper is unwilling to buy stolen goods (how they know they are stolen, I do not know). Is there anyway for me to sell stolen items, without making use of the ...Mon, 07 Sep 2026 14:46:03 -0400https://pop.com.sg/evaluate-the-triple-integral-using-spherical-coordinates.htmlhttps://pop.com.sg/evaluate-the-triple-integral-using-spherical-coordinates.htmlUse spherical coordinates to evaluate the triple integral: $$\iiint_{E}{(x^2+y^2+z^2)dV}$$ Where E is the ball: $E=\left\{(x,y,z)\in \mathbb{R}^3 \mid x^2+y^2+z^2≤49\right\}$....Mon, 07 Sep 2026 14:45:22 -0400https://pop.com.sg/kayle-as-a-support-or-solo-top.htmlhttps://pop.com.sg/kayle-as-a-support-or-solo-top.htmlSo I've played League of Legends since season 1, and after the season ended, we got our Kayle+skin. Ever since than, I haven't seen her being played by anyone. Is there a reason behind that? I thin......Mon, 07 Sep 2026 14:31:39 -0400https://pop.com.sg/why-are-invertible-matrices-called-039-non-singular-039.htmlhttps://pop.com.sg/why-are-invertible-matrices-called-039-non-singular-039.htmlWhere in the history of linear algebra did we pick up on referring to invertible matrices as 'non-singular'? In fact, since the null space of an invertible matrix has a single vector an inverti......Mon, 07 Sep 2026 14:27:02 -0400https://pop.com.sg/is-there-a-game-called-sonic-the-next-level.htmlhttps://pop.com.sg/is-there-a-game-called-sonic-the-next-level.htmlI've been watching the docuseries "High Score" on Netflix, and in episode 4, the Sega episode, there are several clips that refer to something called "Sonic: The Next Level" and a ...Mon, 07 Sep 2026 14:24:02 -0400https://pop.com.sg/division-isn-039-t-associative.htmlhttps://pop.com.sg/division-isn-039-t-associative.htmlConsider the following fraction: $$\frac{\frac{\frac{a}{b}}{c}}{a}$$ How to explain that: $$\frac{\frac{\frac{a}{b}}{c}}{a} \ne \frac{\frac{a^2}{b}}{c}$$ Obviously, you get different results. ......Mon, 07 Sep 2026 14:05:44 -0400https://pop.com.sg/is-it-possible-to-get-the-horadric-cube-with-a-level-lower-than-70.htmlhttps://pop.com.sg/is-it-possible-to-get-the-horadric-cube-with-a-level-lower-than-70.htmlIs it possible to get the cube right at the start of a season journey with level 10 for example?...Mon, 07 Sep 2026 14:03:57 -0400https://pop.com.sg/why-does-it-make-no-sense-to-define-addition-on-points-in-geometry.htmlhttps://pop.com.sg/why-does-it-make-no-sense-to-define-addition-on-points-in-geometry.htmlHere is a simple question: Why does it not make sense to define addition on points in geometry? To be a bit more specific: assume we are talking only about standard Euclidean geometry. It is clea......Mon, 07 Sep 2026 13:56:01 -0400https://pop.com.sg/is-it-possible-to-respec-all-skill-points-duplicate.htmlhttps://pop.com.sg/is-it-possible-to-respec-all-skill-points-duplicate.htmlPossible Duplicate: Is there any way to respec? In town, there is an NPC that lets me respec the last 3 skills I chose, but I want to respec everything. Is there a way to reset my skill point......Mon, 07 Sep 2026 13:53:47 -0400https://pop.com.sg/what-would-be-the-most-significant-way-to-farm-neural-sensors-in-warfr.htmlhttps://pop.com.sg/what-would-be-the-most-significant-way-to-farm-neural-sensors-in-warfr.htmlI've been on a crafting spree in Warframe, and a lot of the things that I am trying to make require 2 at most, which doesn't seem like a lot, but when they are rare drops, it makes it a hassle. Any......Mon, 07 Sep 2026 13:40:08 -0400https://pop.com.sg/how-do-i-kill-the-crab-boss.htmlhttps://pop.com.sg/how-do-i-kill-the-crab-boss.htmlIn the Beach world, the end boss is at least one (I think three, though, if the cutscene is any indication) crab. I have no idea how to fight it! No matter what I do, it seems to hurt me, and I am ......Mon, 07 Sep 2026 13:39:49 -0400https://pop.com.sg/how-to-test-weapons-in-battlefield-3-without-affecting-accuracy-score.htmlhttps://pop.com.sg/how-to-test-weapons-in-battlefield-3-without-affecting-accuracy-score.htmlDo you know of any time when the game is [not] counting the bullets you fire or registering any hits or misses? Would the time when there is this "Waiting for players" message be suitable? The reas......Mon, 07 Sep 2026 13:37:06 -0400https://pop.com.sg/differentiation-of-fractions-and-negative-powers-y-3-sqrt-3-x.htmlhttps://pop.com.sg/differentiation-of-fractions-and-negative-powers-y-3-sqrt-3-x.htmlI am stuck with this concept, just can't get my head around it. I am differentiating fractions and negative powers, I have this question to solve which I just cannot figure out: $$y=-3/\sqrt[3]{x}......Mon, 07 Sep 2026 13:30:02 -0400https://pop.com.sg/software-to-explore-abstract-algebra-and-or-category-theory-closed.htmlhttps://pop.com.sg/software-to-explore-abstract-algebra-and-or-category-theory-closed.htmlIs there any software that lets one explore group theory, ring theory, and category theory visually and theoretically that is tailored for education purposes? I'm not talking about using software l......Mon, 07 Sep 2026 13:17:16 -0400https://pop.com.sg/integral-of-cosh-3-x.htmlhttps://pop.com.sg/integral-of-cosh-3-x.htmlWhat is the integral of $\cosh^3(x)$? And how exactly can I calculate it? I've tried setting $\cosh^3(x)=(\frac{e^x+e^{-x}}{2})^3$ but all I get in the end is one long fraction....Mon, 07 Sep 2026 13:16:30 -0400https://pop.com.sg/where-can-i-see-the-approval-rating-of-my-companions.htmlhttps://pop.com.sg/where-can-i-see-the-approval-rating-of-my-companions.htmlI'm pretty much constantly seeing notifications like "Solas approves" or "Cassandra disapproves", but I still have no idea on how much my companions approve or disapprove of myself in general. I as......Mon, 07 Sep 2026 13:16:12 -0400https://pop.com.sg/why-the-axioms-for-a-topological-space-are-those-axioms.htmlhttps://pop.com.sg/why-the-axioms-for-a-topological-space-are-those-axioms.htmlThis question might have even been asked here before, I don't really know, so sorry if it's duplicate. I've started to study topological spaces and I've found the axioms for such spaces kind of har......Mon, 07 Sep 2026 13:15:07 -0400https://pop.com.sg/concave-down-increasing-example.htmlhttps://pop.com.sg/concave-down-increasing-example.htmlI'm looking for a concave down increasing-function, see the image in the right lower corner. Basically I need a function f(x) which will rise slower as x is increasing. The x will be in range of [......Mon, 07 Sep 2026 13:13:33 -0400https://pop.com.sg/proving-existence-of-inverse-function-using-the-rule-of-differentiatin.htmlhttps://pop.com.sg/proving-existence-of-inverse-function-using-the-rule-of-differentiatin.htmlI am working from a textbook that gives us that The derivative of the inverse function is $$ \frac{dx}{dy} = \large{\frac{1}{\frac{dy}{dx}}}.\qquad (*)$$ $$$$ Now I am stuck on part $(a)$ of the ...Mon, 07 Sep 2026 13:03:24 -0400https://pop.com.sg/questions-tagged-chinese-remainder-theorem.htmlhttps://pop.com.sg/questions-tagged-chinese-remainder-theorem.htmlQ&A for people studying math at any level and professionals in related fields...Mon, 07 Sep 2026 12:58:11 -0400https://pop.com.sg/when-to-use-which-z-score-equation.htmlhttps://pop.com.sg/when-to-use-which-z-score-equation.htmlin some exam past papers I have been doing I have come across the statistics equation z=(sample mean - mean)/standard deviation as well as the equation z = (sample mean - mean)/(standard devia......Mon, 07 Sep 2026 12:54:30 -0400https://pop.com.sg/resultant-from-40-n-and-30-n-vectors.htmlhttps://pop.com.sg/resultant-from-40-n-and-30-n-vectors.htmlIf $F_1$ has magnitude 30 N and $F_2$ has magnitude 40 N, what is the exact magnitude and direction of the resultant vector? I think I should apply the Pythagorean theorem to get the magnitude, so......Mon, 07 Sep 2026 12:34:26 -0400https://pop.com.sg/how-do-you-unlock-the-4-extra-characters.htmlhttps://pop.com.sg/how-do-you-unlock-the-4-extra-characters.htmlIn Super Mario Party, you have 4 extra characters that are locked at the beginning of the game. Without a single player mode to speak of, how do you unlock them?...Mon, 07 Sep 2026 12:08:46 -0400https://pop.com.sg/in-which-branch-of-mathematics-does-logarithm-belong-arithmetic-or-alg.htmlhttps://pop.com.sg/in-which-branch-of-mathematics-does-logarithm-belong-arithmetic-or-alg.htmlI'm currently working on an iOS & Android application for GCE O Level students. I have to classify everything neatly such that Maths never appears to be a messy subject to study and so should I ...Mon, 07 Sep 2026 12:08:10 -0400https://pop.com.sg/application-of-cauchy-davenport.htmlhttps://pop.com.sg/application-of-cauchy-davenport.htmlLet $ p $ be a prime number and $ A \subset \mathbb{Z}/p\mathbb{Z} $. Suppose $ 0 \notin A $ and for $ a \in A $ define $ d(a)= \min\{k|-a \in \underbrace{A+A+ \dots +A}_\text{k times} \} $. I wan......Mon, 07 Sep 2026 12:06:33 -0400https://pop.com.sg/how-to-fix-mouse-slow-sensitivity-in-minecraft-java.htmlhttps://pop.com.sg/how-to-fix-mouse-slow-sensitivity-in-minecraft-java.htmlI have a problem with my mouse control since yesterday. When I move my mouse the screen moves slowly like a movie animation. I don't know what to do. I clicked every buttons in Minecraft. Do I need......Mon, 07 Sep 2026 12:02:28 -0400https://pop.com.sg/is-gts-on-pokemon-oras-unsafe.htmlhttps://pop.com.sg/is-gts-on-pokemon-oras-unsafe.htmlI have been going everywhere for some tips on Pokemon ORAS and everyone is saying that Pokemon GTS is unsafe. I want to know why because I've been thinking of putting up Shiny Pokemon, and I don'......Mon, 07 Sep 2026 12:02:24 -0400https://pop.com.sg/cycle-decomposition-into-disjoint-cycles.htmlhttps://pop.com.sg/cycle-decomposition-into-disjoint-cycles.htmlIn this link here it says that a cycle be decomposed a product of disjoint cycles. However say you consider the element of $S_4$ (The symmetric group of order 24) given by $(12)(13)(14) = (1432)$. ......Mon, 07 Sep 2026 12:00:32 -0400https://pop.com.sg/how-do-i-make-it-so-when-one-player-dies-everyone-dies.htmlhttps://pop.com.sg/how-do-i-make-it-so-when-one-player-dies-everyone-dies.htmlI'm trying to make something like the life link challenge for a realm but can't use a plugin on it so I've been trying to make it using command blocks. it's in 1.14.4 so old commands won't work...Mon, 07 Sep 2026 11:50:35 -0400https://pop.com.sg/how-to-neutralise-eliminate-lydia-boyle-without-attracting-any-guards-.htmlhttps://pop.com.sg/how-to-neutralise-eliminate-lydia-boyle-without-attracting-any-guards-.htmlSo... when you do the "Lady Boyle's Last Party" Mission, and you do not have shadow kill, and your given target is Lydia Boyle (the one in red), you will be led to music room. There, she will ask y......Mon, 07 Sep 2026 11:41:37 -0400https://pop.com.sg/what-is-the-best-set-up-for-insane-mode-in-castle-crashers.htmlhttps://pop.com.sg/what-is-the-best-set-up-for-insane-mode-in-castle-crashers.htmlI'm pretty new to this game and I got to insane mode(my friend helped me) but when I play on insane mode it seems that I'm under powered.(and I don't know how to juggle that well) So I was wonderin......Mon, 07 Sep 2026 11:37:46 -0400https://pop.com.sg/how-to-take-the-derivative-of-a-power.htmlhttps://pop.com.sg/how-to-take-the-derivative-of-a-power.htmlSo I'm trying to solve this problem: Take the derivative of $2^{t^{3}}$ This is the relevant text from my textbook which makes sense to me. The trick seems to convert anything in the form of $b^......Mon, 07 Sep 2026 11:30:11 -0400https://pop.com.sg/sine-and-cosine-power-series.htmlhttps://pop.com.sg/sine-and-cosine-power-series.htmlI have read that sine and cosine can be represented as power series. Power series, as I understand them, are infinite series that can be represented as: $\sum_{j=0}^{\infty} a_j (x-x_0)^j$ where ......Mon, 07 Sep 2026 11:28:03 -0400https://pop.com.sg/why-can-039-t-i-change-my-skin.htmlhttps://pop.com.sg/why-can-039-t-i-change-my-skin.htmlI play Minecraft PE on my Kindle Fire, however, I cannot change my skin; It is staying on the default, Alex. Does anyone know how I might go about fixing this? The version I'm running is MCPE 16.2...Mon, 07 Sep 2026 11:23:06 -0400https://pop.com.sg/calculating-sample-size-for-a-one-sample-dichotomous-outcome.htmlhttps://pop.com.sg/calculating-sample-size-for-a-one-sample-dichotomous-outcome.htmlI'm trying to calculate a required sample sizes for a project using a one sample, dichotomous outcome formula. I'm confused by the intuition of the formula where a less probable result requires fewer ...Mon, 07 Sep 2026 11:18:19 -0400https://pop.com.sg/integral-dependence.htmlhttps://pop.com.sg/integral-dependence.htmlA module theoretical equivalence of integral dependence states as follows: Let $S$ be a ring and $R \subseteq S$ be a subring, and $1\in R$. Then $x \in S$ is integral over $R$ if and only if $R[x......Mon, 07 Sep 2026 11:14:33 -0400https://pop.com.sg/what-is-the-minimum-degree-of-a-polynomial-given-the-initial-condition.htmlhttps://pop.com.sg/what-is-the-minimum-degree-of-a-polynomial-given-the-initial-condition.htmlA polynomial $ p(x)$ is such that $p(0) =5, p(1) = 4, p(2) = 9 $ and $p(3) = 20 $. What is the minimum degree it can have? The problem can easily be solved by hit and trial method. First assuming......Mon, 07 Sep 2026 11:07:05 -0400https://pop.com.sg/need-examples-to-understand-choice-function-and-choice-structure.htmlhttps://pop.com.sg/need-examples-to-understand-choice-function-and-choice-structure.htmlWould you please give me a concrete example for the following definitions? Specifically I don't understand why a choice function is defined as $c: B \rightarrow P(X)$. For any nonempty set $X$, le......Mon, 07 Sep 2026 11:06:50 -0400https://pop.com.sg/how-do-you-interact-with-the-green-plant-like-things.htmlhttps://pop.com.sg/how-do-you-interact-with-the-green-plant-like-things.htmlThese: They can be found in the walls and ceilings all throughout the game and seem to be the key to access the last bits of collectibles, at least as far as I can see. They seem to be places as ......Mon, 07 Sep 2026 11:03:42 -0400https://pop.com.sg/why-is-the-definition-of-inner-product-the-way-it-is.htmlhttps://pop.com.sg/why-is-the-definition-of-inner-product-the-way-it-is.htmlI have recently started looking at inner products. However, I'm still struggling to intuitively understand the definition. I am aware that in most cases we generalize concepts because they are use......Mon, 07 Sep 2026 10:47:29 -0400https://pop.com.sg/do-you-have-to-kill-dean.htmlhttps://pop.com.sg/do-you-have-to-kill-dean.htmlI'm in the Sierra Madre (Dead Money add-on), and I was trying to be a nice guy -- I really was. But when the time came that I could decide whether to kill my companions or let them live and disable......Mon, 07 Sep 2026 10:47:16 -0400https://pop.com.sg/is-the-thrill-digger-minigame-deterministic.htmlhttps://pop.com.sg/is-the-thrill-digger-minigame-deterministic.htmlIn Skyward Sword, in the Edlin Volcano area near the Bokoblin tower, there is a cave where one can play the game Thrill Digger. My question is: can one predict the layout of the board based on: ...Mon, 07 Sep 2026 10:37:20 -0400https://pop.com.sg/derivative-of-natural-log-vs-base-10-log.htmlhttps://pop.com.sg/derivative-of-natural-log-vs-base-10-log.htmlConsider the logarithmic function with base $10.$ $$ y=\log{\left(x\right)} $$ wherein the derivative with respect to $x$ is: $$ f'\left(x\right)=\frac{1}{x} $$ Now consider the natural logarith......Mon, 07 Sep 2026 10:26:43 -0400https://pop.com.sg/database-of-fol-statements-and-proofs.htmlhttps://pop.com.sg/database-of-fol-statements-and-proofs.htmlIs there a database somewhere of simple FOL statements, with their proofs written out in a Hilbert-style deduction system, or perhaps a tool to take such statements and produce proofs? While I see ...Mon, 07 Sep 2026 10:21:37 -0400https://pop.com.sg/the-final-state-of-1000-light-bulbs-switched-on-off-by-1000-people-pas.htmlhttps://pop.com.sg/the-final-state-of-1000-light-bulbs-switched-on-off-by-1000-people-pas.htmlThere are 1000 light bulbs and 1000 tutors. All light bulbs are off. Tutor 1 goes flipping light bulb 1,2,3,4... tutor 2 then flips 2,4,6,8... tutor 3 then 3,6,9...etc until all 1000 tutors have ......Mon, 07 Sep 2026 10:18:54 -0400https://pop.com.sg/user-calvin-lin-mathematics-stack-exchange.htmlhttps://pop.com.sg/user-calvin-lin-mathematics-stack-exchange.htmlQ&A for people studying math at any level and professionals in related fields...Mon, 07 Sep 2026 10:17:57 -0400https://pop.com.sg/proving-gradient-of-a-function-is-always-perpendicular-to-the-contour-.htmlhttps://pop.com.sg/proving-gradient-of-a-function-is-always-perpendicular-to-the-contour-.htmlCan someone give an explanation of how such a proof would go, given a function example: $y = f(x)$...Mon, 07 Sep 2026 10:14:54 -0400https://pop.com.sg/what-039-s-the-point-of-a-kingdom-past.htmlhttps://pop.com.sg/what-039-s-the-point-of-a-kingdom-past.htmlIt seems to indicate that you should replicate the Kingdom, based on this image, but nothing seems to happen when you do. What's the point of this image?...Mon, 07 Sep 2026 10:14:03 -0400https://pop.com.sg/what-is-the-relation-between-production-meals-and-total-export-price.htmlhttps://pop.com.sg/what-is-the-relation-between-production-meals-and-total-export-price.htmlI'm playing Tropico 4 right now, but I'm pretty sure it's the same for all Tropico games. I've finished the normal campain, but I'm still wondering what these numbers are about. So let's take an e......Mon, 07 Sep 2026 10:05:07 -0400https://pop.com.sg/why-dominated-convergence-theorem-is-related-to-the-superiority-of-leb.htmlhttps://pop.com.sg/why-dominated-convergence-theorem-is-related-to-the-superiority-of-leb.htmlI read the following paragraph from wikipedia: In measure theory, Lebesgue's dominated convergence theorem provides sufficient conditions under which almost everywhere convergence of a sequence of ...Mon, 07 Sep 2026 09:59:19 -0400https://pop.com.sg/how-to-enable-steam-overlay-while-playing-dungeons-of-dredmor.htmlhttps://pop.com.sg/how-to-enable-steam-overlay-while-playing-dungeons-of-dredmor.htmlFor some reasons I cannot access to Steam overlay and other Steam features (F12->screenshot) while playing Dungeons of Dredmor. Do you know how to fix it? Just to be precise the in-game option in ......Mon, 07 Sep 2026 09:52:45 -0400https://pop.com.sg/for-numbers-divisible-by-three-why-is-the-sum-of-their-digits-able-to-.htmlhttps://pop.com.sg/for-numbers-divisible-by-three-why-is-the-sum-of-their-digits-able-to-.htmlWhen you add the digits of any number that is divisible by three, that sum of those digits also appears to be divisible by three (with no remainder). For example a number (which I randomly grab fr......Mon, 07 Sep 2026 09:48:20 -0400https://pop.com.sg/darboux-theorem.htmlhttps://pop.com.sg/darboux-theorem.htmlDarboux's Theorem states that" If $f$ is differentiable on $[a,b]$ and if $k$ is a number between $f^{\prime}(a)$ and $f^{\prime}(b)$, then there is at least one point $c\in (a,b)$ such that $f^{\p......Mon, 07 Sep 2026 09:27:24 -0400https://pop.com.sg/properties-of-dictionary-order-topology.htmlhttps://pop.com.sg/properties-of-dictionary-order-topology.htmlProperties of dictionary order topology Choose the correct option My attempt : According to Munkres the order topology on $\mathbb{R} \times \mathbb{R}$ has as basis the collection of all ......Mon, 07 Sep 2026 09:24:48 -0400https://pop.com.sg/getting-attributes-bonuses-5-5-5-in-elder-scrolls-oblivion.htmlhttps://pop.com.sg/getting-attributes-bonuses-5-5-5-in-elder-scrolls-oblivion.htmlI have just completed the recommended quests for the Mages Guild to get accepted into the Arcane University. Now, I think it's time to work on leveling up the mage class character that I have. I'm ...Mon, 07 Sep 2026 09:16:41 -0400https://pop.com.sg/how-to-prove-that-mathbb-z-2z-times-z-2z-is-not-cyclic.htmlhttps://pop.com.sg/how-to-prove-that-mathbb-z-2z-times-z-2z-is-not-cyclic.htmlHow to prove that $\mathbb{Z/2Z\times Z/2Z}$ is not cyclic? Here is what I did, what is wrong with it if anything and is there a better way to prove it? A group $G$ is cyclic if $\exists\ a \in G$ ......Mon, 07 Sep 2026 08:44:47 -0400https://pop.com.sg/steam-purchase-issue.htmlhttps://pop.com.sg/steam-purchase-issue.htmlWhen you attempt to purchase Realm of the Mad God's "Beginner's Package", it lists the purchase as buying "2600 Gold". The package contains more than just gold, so what does this mean?...Mon, 07 Sep 2026 08:42:36 -0400https://pop.com.sg/finding-the-measure-of-an-angle-given-area-and-diameter.htmlhttps://pop.com.sg/finding-the-measure-of-an-angle-given-area-and-diameter.htmlAlright, so i've been trying to tackle this problem. The answer to this problem is 40 degrees (3). Now i'm trying to figure out how. I decided to start with finding the area of the whole circle wh......Mon, 07 Sep 2026 08:33:44 -0400https://pop.com.sg/how-do-i-set-a-kill-command-on-a-block.htmlhttps://pop.com.sg/how-do-i-set-a-kill-command-on-a-block.htmlYou can set a /kill command on a command block, I know that, but how do I do it? I am making a map, so please help!...Mon, 07 Sep 2026 08:28:24 -0400https://pop.com.sg/area-enclosed-between-3-curves.htmlhttps://pop.com.sg/area-enclosed-between-3-curves.htmlQuestion: What is the area of the region enclosed by the curves: $$2y = 4\sqrt{x},\quad y = 3,\quad \text{and} \quad 2y + 2x = 6. $$ I have tried calculate all the definite integrals but I am not ......Mon, 07 Sep 2026 08:16:18 -0400https://pop.com.sg/why-do-some-players-play-league-of-legends-in-window-mode.htmlhttps://pop.com.sg/why-do-some-players-play-league-of-legends-in-window-mode.htmlWhile watching this current LoL live world championship (Intel extreme masters), I noticed some players play in window mode. Why is that? What are the benefits of playing LoL in window mode?...Mon, 07 Sep 2026 08:07:51 -0400https://pop.com.sg/what-is-the-solution-of-a-2-b-2-closed.htmlhttps://pop.com.sg/what-is-the-solution-of-a-2-b-2-closed.htmlHow to solve $a^2=b^2$? Should I consider if the number is negative or positive?...Mon, 07 Sep 2026 08:02:27 -0400