There came a situation in one game where there was a runner occupying first base (R1) and third base (R3), with one out. The batter then hits a ground ball to the left of the second baseman. He fields the ball and attacks R1, advancing to second base. R1 then stops and back pedals to first base to avoid the tag. The runner the second baseman then throws over to first base to get the battered runner out; with this, R3 advances home, and there is now a hot box between first and second because of R1.   After the runner is tagged at second, the umpire had tried to stop play claiming that because R1 did not just stop but back pedaled to avoid the tag, he is automatically out, and no run scores.  Was the umpire's decision right?
Here's a situation that came up during a back lot league softball game a few weeks ago. (Note: While our league has some of its own rules we try to defer to MLB rules in all causes that aren't specifically addressed.)  There is a runner on second (R2) and a runner on first, with no outs. A ground ball is hit to the third baseman (3B) who cleanly fields the ball away from third base. Seeing that R2 is running toward him, 3B does not go to third and instead waits to tag the incoming R2. R2, in an attempt to buy some time for the other runners, stops advancing to third base. As soon as R2 stops, 3B declares R2 is out (without making a tag) and throws the ball to first to make a play.  During the discussion after the play, the 3B claimed that any player advancing on a force cannot stop moving toward their next bag or they are automatically out (the same way a runner leaving the baseline to avoid a tag is considered out). Our rules don't have a specific clause that addresses this situation and I couldn't find anything in official MLB rules (though it's possible I missed something, as 3B claims it is an MLB rule).  So, is 3B’s claim correct? That if a runner who is forced to advance to their next base stops (in particular to avoid/delay a tag) they are automatically out?
Which arena do free and crown chests use when determining the cards you will get? If I am in arena X when I collect my tenth crown for the crown chest, or a free chest becomes unlocked, then proceed to climb to arena X+1 before opening the chests, which arena will be used to determine the cards I get? Will it use the arena I was in when I unlocked the chests in, or the arena I opened them in? Classify all groups with order $pq$, $p$ is not equal to $q$ I am reading the following material:  . At page 5, there is a proof classifying all groups with order $pq$(they are all primes and $p$ is not equal to $q$). I am lost in the last two sentence, which claims the semidirect product are all isomorphic. Could someone help me to understand it? Thanks! Novel, group transported to a fantasy world, wild/chaos magic I was reading  and was strongly reminded of a series I remember reading in my teens.  This would have been a series of novels (possibly just one), published in English, and likely before 1980 - I read it in the 90s and it was fairly old, a used book.  I do not think it is the same as the linked question, which is why I'm asking this separately.  It was definitely a fantasy, not sci-fi.  Plot:  At least two girls (and possibly also some boys/other girls) are transported from modern Earth into a fantasy world.  I think they're a group of friends, possibly with some romantic pairings, and are in the 16-25 age range.  The first significant scene I remember is two of the girls ending up in a city, where they are taken in by an older female artist (might have been a different creative type, like a sculptor/actress).  She's lesbian/bisexual.  At some point she attempts to give one of the girls a love potion, but they reverse it on her, so instead the artist falls in love with the girl and accompanies her for the rest of the books.  Twist: It's later revealed that the artist's friends recognized the love potion and removed it.  She pretended to be in love and went along because she thought it would be interesting.  At some point at least one of the girls ends up basically being a magical sex slave/prostitute.  I remember her being tattooed or painted - I think in blue - and also possibly given some magical jewellery/piercings that ensure her obedience/love of her owner.  I do not remember much of the over-arching plot, just a few disjointed pieces:  The world has chaos/wild magic storms.  The books might have called them something else.  Anyone or anything caught by these storms is transformed into something else entirely, so different objects or species.  These show up throughout as minor plot encounters.  I think they can be defended against with a special material.  Near the very end, a large storm engulfs a major city, giving it entirely new architecture and transforming the inhabitants into green, hermaphrodites with a centaurish body structure.  I am not 100% sure this was the same novel, but I recall a secondary character with a secret - at night he turns into a woman (not just his body, but an entirely different person).  At some point it's revealed that the woman was his lover, and he saved her life by sharing his body with her - of course, now they can never meet/touch again. Does 10 heads in a row increase the chance of the next toss being a tail? I assume the following is true: assuming a fair coin, getting 10 heads in a row whilst tossing a coin does not increase the chance of the next coin toss being a tail, no matter what amount of probability and/or statistical jargon is tossed around (excuse the puns).   Assuming that is the case, my question is this: how the hell do I convince someone that is the case?   They are smart and educated but seem determined not to consider that I might be in the right on this (argument). Is there a consensus in the mathematical community, or some accepted authority, to determine whether zero should be classified as a natural number?  It seems as though formerly $0$ was considered in the set of natural numbers, but now it seems more common to see definitions saying that the natural numbers are precisely the positive integers. Show that a number has a terminating decimal expansion if and only if, it is rational and when in lowest terms, its denominator is coprime to all primes other than $2$ and $5$.   This is an unsolved question in my lecture notes. I can only seem to prove the converse direction for this. Would appreciate a solution for the other direction.     For converse direction:   Let the number, in lowest terms, be given by $\frac{l}{m}$ where $m = 2^ \alpha 5^\beta$, for some positive integers, $\alpha$ and $\beta$.    If $\alpha &gt; \beta$, let $k = 5^{(\alpha-\beta)}$. If $\alpha &lt; \beta$, let $k = 2^{(\beta-\alpha)}$.   Then $\frac{l}{m} = \frac{kl}{k2^\alpha5^\beta}=\frac{kl}{10^q}$ where $q = \max(\alpha,\beta)$.   Hence $\frac{l}{m}$ is a terminating decimal. Are there any advanced options for Google Chrome's history search? Would someone give a thorough explanation of 1.14 Minecraft's /data modify? I believe there are several ways to prove that $\sum\limits^{\infty}_{n=1}\left(1-\frac{1}{\sqrt{n}}\right)^n$ converges. Can you, please, post yours so that we can learn from you?  HERE IS ONE   Let $n\in\Bbb{N}$ be fixed such that $a_n=\left(1-\frac{1}{\sqrt{n}}\right)^n.$ Then, \begin{align} a_n&amp;=\left(1-\frac{1}{\sqrt{n}}\right)^n \\&amp;=\exp\ln\left(1-\frac{1}{\sqrt{n}}\right)^n\\&amp;=\exp \left[n\ln\left(1-\frac{1}{\sqrt{n}}\right)\right] \\&amp;=\exp\left[ -n\sum^{\infty}_{k=1}\frac{1}{k}\left(\frac{1}{\sqrt{n}}\right)^k\right]\\&amp;=\exp\left[ -n\left(\frac{1}{\sqrt{n}}+\frac{1}{2n}+\sum^{\infty}_{k=3}\frac{1}{k}\left(\frac{1}{\sqrt{n}}\right)^k\right)\right]\\&amp;=\exp \left[-\sqrt{n}-\frac{1}{2}-\sum^{\infty}_{k=3}\frac{n}{k}\left(\frac{1}{\sqrt{n}}\right)^k\right]\\&amp;\equiv\exp \left(-\sqrt{n}\right)\exp \left(-\frac{1}{2}\right)\end{align} Choose $b_n=\exp \left(-\sqrt{n}\right)$, so that  \begin{align} \dfrac{a_n}{b_n}\to\exp \left(-\frac{1}{2}\right).\end{align} Since $b_n \to 0$, there exists $N$ such that for all $n\geq N,$ \begin{align} \exp \left(-\sqrt{n}\right)&lt;\dfrac{1}{n^2}.\end{align} Hence, \begin{align}\sum^{\infty}_{n=N}b_n= \sum^{\infty}_{n=N}\exp \left(-\sqrt{n}\right)\leq \sum^{\infty}_{n=N}\dfrac{1}{n^2}&lt;\infty,\end{align} and so, $\sum^{\infty}_{n=1}b_n&lt;\infty\implies \sum^{\infty}_{n=1}a_n&lt;\infty$ by Limit comparison test. Give read-only access to specific folders? Why do you have to use copy_to_user()/copy_from_user() to access user space from the kernel? How to show every field is a Euclidean Domain. I'm having trouble proving this. This is what I have so far:  Let $F$ be a field. Let $v(x) \rightarrow 1$ for all $x$ not equal to $0$.  So if we let $x$ be in $F$ where $x$ not zero then we can write $x$ as: $x=qy+r$ for some $y$ in $F$. If $r$ not zero then $V(r)=1$.  Not sure what to do from here. I know eventually I'm supposed to get no remainder $(r=0)$ but I'm stuck at applying the definition and valuation map. Can I insert an image into an equation? I would like to use a small image in an equation, where a symbol like \alpha might otherwise be. Is there a nice way to do this? Searching by user id in Android app only shows questions, no answers I have a Samsung Galaxy S3. Android version 4.3  I downloaded the official StackExchange app today. I am not able to view post related to android tag from my profile. I tried refreshing also  Snap     Edit:  However i am able to see one post for the relevant from the drop down list    Edit 2:  I tried what Steven V suggested. However it's the same.    I tried for a different user its the same. Privilege progress indicator interferes with (old) Stack Exchange dropdown I know I'm late with this; this could be the last bug report about the old topbar. But the text on the privilege progress indicator (on your profile page) appears above the dropdown menu coming from the Stack Exchange button, as can be seen in the picture below.     Changing the z-index property of .s-progress-bar._badge .-info, .s-progress-bar._privilege .-info from 2 to 1 solves the problem.    The new menu seems to have a high enough z-index so that this is no longer a problem anymore: Which is correct?   Sheila and Angie are wearing the same shirt today.  Sheila and Angie are wearing the same shirts today. Sheila and Angie are wearing same shirts today. Please add close flags, duplicate links and review data to the public data dump Did Dolores Umbridge Have Any Association with Voldemort (or Death Eaters) before His Return? Merging Raster Datasets of Different Resolutions using ArcGIS Desktop? I am using ArcGIS Desktop.  I have two DEMs in .tif format and I am looking to merge the two. The main problem with merging these are that they are different resolutions (one is 10m and one is ~20m). Also, another problem with merging the two is that they overlap and I am not sure of the most effective way of dealing with that overlap. Obviously I want to keep the values of the better resolution.   So what are the best methods here?   Is there a python script available that works best with merging rasters? I would like to automate this with a script if possible. Which process of resampling is best for DEM data? Bipolar, Cubic... ? What is the best way to merge overlapping DEMs? Rotating image / marker image on Google map V3