Do items which add to some ability affect your skill modifier?
If a PC's ability score increases due to an item, does it increase the corresponding modifier for the ability score or any skills/attacks?
Question: Can anyone shed some light on this formula? I can't find any information on it.  It has three corollaries that I also need to understand: Hero rescues a minor deity, granted a wish of small value; gets a girl As a high school student just starting in science fiction, I read a short story collection in paperback that included this story – not quite a short-short, but not very long either.  I think that it was written by a familiar author, since the collection was one of those “Best Of…” anthologies.    Our hero is a sympathetic young guy trying to get ahead, in love with a beautiful neighbor, but hopeless in love.  He rescues a miniature Minor Deity (and I've forgotten the mechanism – rescued from a cat perhaps?) and gets a wish in return.  The catch is that since this is only a minor deity, the value of the wish is small – and I forget the actual value, perhaps $2.49.  He asks for help winning at the races to help get the girl – and the minor deity says sure, but the payoff can only be $2.49.  How about help rescuing her from a calamity like an earthquake?  Sure, but the total damage can only be $2.49. Other alternatives are discussed, but the value can only be $2.49. Frustrated, our hero thinks about the problem, but the Minor Deity thinks he has a solution.    Later that evening, the girl knocks on the door, he opens it to her welcoming arms, and the night passes.  The next morning, our hero finds a small clipping on the floor, an article stating the latest estimates of the total value of the elements in the human body were… $2.49.  (The whole story was building to that punch line.) Determining the structure of the quotient ring $\mathbb{Z}[x]/(x^2+3,p)$ What is the relative speed of two near-light speed particles headed towards each other? I understand that nothing can move faster than light due to time dilation. I want to build upon my understanding of Einstein's theory of Special Relativity, so I came up with this hypothetical problem for myself:  If both particles are moving at 0.9c towards each other (according to an observer on Earth), what speed does each particle have relative to the other?  I'm stumped since I am only familiar with Newtonian classical mechanics to solve this (which would be wrong). I am aware of Lorentz' factor $\gamma =\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$ and the time dilation equation $t_m = \frac{t_o}{\sqrt{1 - \frac{v^2}{c^2}}}$, but I'm not sure how to apply it in this instance. I'm just looking for a gentle push in the right direction. Edit: My prior research:  This article, ,  talks about the effect of a baseball thrown at 0.9c would have as it traveled towards a batter. This is not what I'm looking for since it doesn't explain the math behind finding the collision speed between two high velocity entities.  This question on Yahoo, , asks a similar question to mine, but no math is involved to demonstrate the calculations behind the reasoning.  This question on Physics.SE, , does not answer my question either. I have not been able to find a similar Physics.SE question which can provide me to clues to my own hypothetical question.  I have also Googled the following phrases:    i. &quot;collision faster than the speed of light&quot; ii. &quot;collision of high speed particles&quot; iii. &quot;lorentz transformation in a collision&quot; iv. &quot;collision analysis at light speed&quot; I am a computer scientist, and one of my professors today used the symbol $\propto$. I tried to search that using google, but it returns no results, and I do not even know its name.  So, I would like to ask, what does the operator $\propto$ mean? What is its name, and how is it used? 3 more votes from other users are needed to close this question.   This is the message I got hovering the mouse over close voting tab.   I wonder can we begin any sentence with a numeric value? Is it good practice? Multivariable limit proof: $\lim\limits_{(x,y)\rightarrow (0,0)}\frac{\left|x\right|^a\left|y\right|^b}{\left|x\right|^c + \left|y\right|^d} = 0$ Note: Suppose $f(z)$ is a polynomial or a proper/strictly proper rational function.   Can someone demonstrate why if all coefficient of $f(z)$ are real then relation $f(\bar z)$ = $\bar {f(z)}$ hold  Is there a theorem for this result? When should end punctuation go inside quotes? Understanding DC-DC boost converters I’m currently working on a solar powered boat with a modest sized team of people. For our competition we are only allowed to have 3 12v batteries on board but we are allowed to have up to 52v at any point in our setup. We are hoping to kick up the speed of our outboard motor for the sprint portion of the completion and are looking into using a boost converter for this.   After doing a little research I’m a bit confused about how they fundamentally work. From what I can tell they take in a voltage and current and put out a higher voltage with a lower current with some level of efficiency. But it seems to be independent from the load( in this case the motor) which doesn’t make much sense to me because I thought the current would be determined by whatever my load is. How do loads actually interact with boost converters?( The simpler the better.)  For reference we are using the Saietta 119r motor system and I’m considering using the MPS MPQ3425 boost converter. How can I programmatically force-stop scrolling in a UIScrollView? A local IP address (RFC 1918) on my network that is not … local I've noticed an IP address today on my network (192.168.15.1) which when visited actually goes to a page that has a router webconfig page (Not my router)  The puzzling thing is that i tried traceroute 192.168.15.1 which said that the distance between me and that host is 9 hops, whereas the distance between me and any other computer on my home network is 2 hops away (My computer --> Router --> Host)   Can someone please explain what's going on here ?  tracert output:  Tracing route to 192.168.15.1 over a maximum of 30 hops    1    &lt;1 ms    &lt;1 ms    &lt;1 ms  192.168.1.1   2    47 ms    51 ms    49 ms  [163.121.171.123]   3     *        *        *     Request timed out.   4   128 ms     *        *     163.121.211.134.dnet.net [163.121.211.134 ]   5     *      134 ms   126 ms  10.37.242.18   6    94 ms    90 ms    95 ms  10.35.2.157   7   178 ms   254 ms   206 ms  10.32.8.107   8    85 ms    57 ms   318 ms  10.35.0.186   9   215 ms   241 ms   230 ms  192.168.15.1  Trace complete. I had just arrived at the hotel, checked in and gotten into my room. Just as I was about to unpack, I noticed that one of my bags was missing. At first I thought I had left it back at the airport, but it turned out that I had left it on the taxi.  Here, what's the meaning and role of "just"?  Why do you guys input the word "just" here?  What exactly does the word do grammatically?   Could you help me? Let's say I have two planets that are one hundred thousand lightyears away from each other. I and my immortal friend on the other planet want to communicate, with a strong laser and a tachyon communication device.  I record a message on the tachyon communication device and release the message at exactly the same time as I activate the laser, both of which are directed to the other planet which is one hundred thousand lightyears away. Say it is the year 0 for both of us at the time I did this.  If tachyons existed, then the message would arrive to my friend before the photons in the laser. It would arrive, say, a thousand years earlier. From my vantage point, that message will arrive to her at year 99,999; the same would be true for my friend's vantage point. However, she will only see the laser at year 100,000.  So since she got the message at year 99,999, she immediately sends me a reply back going through the same procedure as I did. She records a message and releases it at the same time as the laser. The tachyons will arrive 1,000 years earlier than the laser, so for me, I will receive the message at year 199,998. I will receive the laser, however, at year 199,999.  It seems to me that communication this way does not violate causality. I will still have received the message after I had sent it.   If tachyons truly violated causality, though, I realize it should arrive at year -1 for her, and so she can reply to me at year -2, which would mess me up by year 0 as I will ask her how she knew I was planning on sending her a message before I sent it. I could send her a different message, which she would end up receiving at year -1, and will end up confusing her as she would have received one message asking her out, and the other asking her how did she know I was asking her out. She then decides I am crazy and sends me a message at year -2 that she does not want to date me, and so she will have both turned me down and entertained me before I have even asked her out.  On the other hand, let's go back to year 0 and add a third device to our list: an Alcubierre drive. After I send out the message and the laser, I get impatient and do not feel like waiting 99,999 years, so I get on my Alcubierre drive spaceship and arrive on her planet at the same year 0. My friend is not in her office, so I leave a note to her also immortal secretary saying I dropped by and that she should expect a message for her in year 99,999.  I then get back on my Alcubierre drive and land back on my planet, still on year 0. Meanwhile, the tachyons and photons I sent out are still racing to arrive to her. By year 99,999, she receives the message just as I Alcubierre drive back to her, and I pick her up for dinner.  But the point of my question is, it seems to me that just going faster than light, if that alone was what you had, would not violate causality. It must be something else. I understand time dilation and that things with mass cannot travel at the speed of light, but using the Alcubierre drive, hypothetically speaking, I was still able to outpace the photons while also having mass. It still did not produce causality problems. Alcubierre drives are also valid solutions to GR.  It seems circular to me to say that what makes traveling faster than light violate causality is because it violates causality (if faster than light communication was divorced from causality problems, then the causality problem would cause itself -- thereby violating causality and, hence, we would scrap it and conclude that there is no causality problem after all).  What is it that I am missing? If someone could help me out, that would be excellent. I've been itching to ask my friend out for a few millenia now. :) Why is quadratic integer ring defined in that way? Quadratic integer ring $\mathcal{O}$ is defined by \begin{equation}    \mathcal{O}=\begin{cases}       \mathbb{Z}[\sqrt{D}] &amp; \text{if}\ D=2,3\ \pmod 4\\       \mathbb{Z}\left[\frac{1+\sqrt{D}}{2}\right]\  &amp; \text{if}\ D=1\pmod 4    \end{cases} \end{equation} where $D$ is square-free.   I understand $\mathbb{Z}\left[\frac{1+\sqrt{D}}{2}\right]$ is not closed under multiplication if $D=2,3\pmod 4$. But still, isn't it more natural to define $\mathcal{O}=\mathbb{Z}[\sqrt{D}]$ for all square-free $D$? (in that case, it really seems like 'quadratic integer') I wonder what is the motivation of this definition. Property of Entire Functions How to update the PATH user environment variable from command-line Let $(a_n)$ be a strictly increasing sequence of positive integers such that: $a_2 = 2$, $a_{mn} = a_m a_n$ for $m, n$ relatively prime. Let $(a_n)$ be a strictly increasing sequence of positive integers such   that: $a_2 = 2$ and $a_{mn} = a_m a_n$ for $m, n$ relatively prime. Show that $a_n = n$, for every positive integer $n$.   This is a result apparently due to Paul Erdős, and  has a proof by induction.  I tried like this, $a_{10}=a_2a_5$. After this what we can do?    [Editor's comment] Possibly due to the apparent simplicity of the conditions it may be difficult to appreciate the subtleties of this question. If we try and construct a counterexample like $a_3=4$, $a_4=5$, $a_5=6$, then the requirements dictate $a_6=8$, $a_{10}=12$, $a_{15}=24$. At this point we realize that we have been speeding. For monotonicity forces $a_9\le 11$, and therefore $a_{18}\le22&lt;a_{15}$, violating the requirements. It is not obvious why something similar ruins all the modifications to the sequence $a_n=n$. [/comment, JL] pdfTeX error (font expansion): auto expansion is only possible with scalable Does IBIS reduce image resolution? How does it compare to lens based IS?