Javascript Decimal Subtract
Is floating point math broken?
Is it OK to call a professor by his first name when he/she signs emails by only first name? If a professor in a North American country presents his- or herself by his/her first name in email messages, does this mean that students can refer to him/her by his/her first name? Or is this generally not a good idea, unless the professor has explicitly mentioned that he/she can be referred to by first name? I've noticed that most professors, who prefer to be referred to more formally, do not sign their emails with just their first names, but usually initials or first and last name. Submodule of free module over a p.i.d. is free even when the module is not finitely generated? Possible Duplicate:          In  the following claim was mentioned:  $R/I \otimes_R M \cong M / IM$  So I tried to prove it. Can you help me finish my proof? Thanks!    We recall that $M \otimes_R -$ is a covariant right-exact functor that it is exact if $M$ is flat and we observe that the following is an exact sequence: $$ 0 \to IM \xrightarrow{i} M \xrightarrow{\pi} M / IM \to 0$$  $R/I$ is an $R$ module since $R/I$ is a subring of $R$ closed with respect to multiplication from $R$ but it is not necessarily flat hence we only get exactness on one side:  $$  (R/I) \otimes_R IM \xrightarrow{id \otimes i} (R/I) \otimes_R M \xrightarrow{id \otimes \pi} (R/I) \otimes_R M / IM \to 0$$  Then $$ \mathrm{Im(id \otimes \pi)} = (R/I) \otimes_R M / IM  \cong (R/I) \otimes_R M / \mathrm{Ker} (id \otimes i) $$  so we want to show two things:   (i) that $\mathrm{Ker} (id \otimes i) = \{0\}$. To this end let $r + I \otimes im \in (R/I) \otimes_R  IM $ and assume $ id \otimes i(r + I \otimes im ) = r + I \otimes im = 0 + I \otimes 0$. I'm not sure how to proceed from here.   (ii) and that $M /IM \cong (R/I) \otimes_R M / IM $  Can you help me? Thanks. I'm curious how USB device recognition works in Windows. I imagine it's something like this:   When you plug in a device, it tells Windows "here's my device ID to tell you what I am" Windows looks to see if any drivers have been installed that match that device ID. The driver probably tells Windows what the device should be called - like "BlackBerry Curve" or "Canon Printer" If so, it somehow associates that device with that driver Otherwise, it looks for a matching driver online (if you let it)   Am I right? If so, that still leaves some questions.   When you install drivers, where do they go? Are they files in a folder, or do they get added to the registry? What is Windows doing when it first recognizes the device, thinks, and finally says "your new device is installed and ready to use?" Where does Windows look for missing drivers? Is it in their own database? Do device manufacturers submit drivers to Microsoft for inclusion there?   Can anybody explain how this process really works? Also, do other OSes do this differently? Do images uploaded to imgur.com have any backup? How do you Set Custom Time in Ubuntu? One of the achievements for the Thieves Guild says "Restore the Thieves Guild to its former glory."  Brynjolf doesn't say anything to me, I can't seem to find Karliah, and as far as I can tell, I am finished with the plotline quests for the Thieves Guild. All I have left available are repeatable quests from Vex and Delvin.  How can I get this achievement? CommonMark regression: image embed exclamation sign syntax broken after  tag $\Bbb{Z}_{26} \rtimes_{\alpha} \Bbb{Z}_{5} \cong \Bbb{Z}_{26} \times \Bbb{Z}_{5}$ as groups. What is a smart pointer and when should I use one? What is a smart pointer and when should I use one? Does blocking an attack with the Shield spell still trigger Armor of Agathys? I am contemplating a Oath of Conquest Paladin / Sorcerer multiclass character, with a 1 level dip in hexblade warlock. This character will have access to the Armor of Agathys and Shield spells, which potentially allows for a pretty nice combo. The Shield spell states (PHB 275):  Casting Time: 1 reaction, which you take when you are hit by an attack or targeted by the magic missile spell... Until the start of your next turn, you have a +5 bonus to AC, including against the triggering attack,  It looks like you are indeed hit by an attack, but since you have a bonus to AC, you can potentially force that attack to miss instead. Armor of Agathys states (PHB 215),  If a creature hits you with a melee attack while you have these hit points, the creature takes 5 cold damage.  If I cast Shield and cause an attack that &quot;hit&quot; me to miss, does Armor of Agathys still deal damage? I am leaning toward yes, though this combo seems a little too strong--Shield is already a strong spell, and this character will eventually have 9 1st level spell slots and a 7th level spell slot. Not only can they freely block attacks with Shield, but they can also deal up to 35 (5d10) damage to the attacker without an attack roll or saving throw. While a Warlock would have to spend both of their spell slots to do this once, my character would be able to do this 4 times with spell slots to spare. Some notes:    ask about reducing the damage from a confirmed hit to zero. This question is asking about what happens when the Shield spell causes the attack to miss entirely. A number of online resources, such as the Roll20 5th edition compendium, seem to be missing the correct casting time for the Shield spell. Answerers should make sure they're looking at the correct version from the PHB. What is the correct name to use with /give for Lapis Lazuli? In Minecraft, when cheats are enabled you can give yourself items using the command /give [user] [item] [count], e.g. /give user45623 dirt 32. What is the item name to use for Lapis Lazuli? I've tried lapis_lazuli, lapis, lazuli, dye4, and dye_4, but it's none of those. Coming from SketchUp one of the tools I miss most is the circle draw tool which lets you draw a circle on any face and then you could extrude it in/out. The only tool that I know of that comes close to this is the knife tool but this would be very impractical to cut out with the knife  Example:    Is there any tool in blender that can match this function? also how could you do this with squares? What does it mean for two objects to "touch"? If you've ever been annoyingly poked by a geek, you might be familiar with the semi-nerdy obnoxious response of      "I'm not actually touching you! The electrons in the atoms of my   skin are just getting really close to yours!"   Expanding on this a little bit, it seems the obnoxious geek is right. After all, consider Zeno's paradox. Every time you try to touch two objects together, you have to get them halfway there, then quarter-way, etc. In other words, there's always a infinitesimal distance in between the two objects.   Atoms don't "touch" each other; even the protons and neutrons in the nucleus of an atom aren't "touching" each other.  So what does it mean for two objects to touch each other?   Are atoms that join to form a molecule "touching"? I suppose the atoms are touching, because their is some overlap, but the subatomic particles are just whizzing around avoiding each other. If this is the case, should "touching" just be defined relative to some context? I.e, if I touch your hand, our hands are touching, but unless you pick up some of my DNA, the molecules in our hands aren't touching? And since the molecules aren't changing, the atoms aren't touching either?  Is there really no such thing as "touching"? limit of Holder norms: $\sup\limits_{x\in [a,b]} f(x) = \lim\limits_{n\rightarrow\infty} \left(\int_a^b (f(x))^n \;dx\right)^{\frac{1}{n}}$ Show that $$\sup_{x\in [a,b]} f(x) = \lim_{n\rightarrow\infty} \left(\int_a^b (f(x))^n \;dx\right)^{\frac{1}{n}}$$ for f continuous and positive on [a,b].  I can show that LHS is greater than or equal to RHS but I can't show the other direction. Adding shapefile or feature class as layer in ArcMap using ArcPy Today, after returning from vacations, I started my QGIS 1.7 and got this terrible message:    Help, anyone? Shorter way to say "conversational partner" I'm looking for a proper English word to say "conversational partner".   Is "interlocutor" a word an average person would understand?  Are there any other words or shorter expressions which could describe a person you are having a conversation with, but who is not your friend and is basically unknown to you? When and why is the [featured] tag removed by the Community user? I've found that the Meta (moderator only) tag  is automatically  by the  user. So, I want to know when and why is the tag  is removed by this user?  Is there any mechanism for this removal or is there simply a specified time period after which the  is automatically removed by the Community user? One of the most commonly asked questions of beginners. How do ranks work in Go for amateurs?  Why do we start backwards? And why do we suddenly count upwards again? What is the difference between 9d and 9p? How is this related to rating? What are the basic differences between ranks used in different countries and different servers?