Why does $0/0$ have to be undefined?
Explanation of method for showing that $\frac{0}{0}$ is undefined
Is there any hint of of the first Wizarding War being an international event? Why do electrons around nucleus radiate light according to classical physics As I navigate through physics stackexchange, I noticed .  Electrons radiate light when revolving around nucleus? Why is it so obvious?  Note that I do not know anything about quantum mechanics - and I just want classical stories. How to show that $\mathbb{Q}$ is not $G_\delta$ I read a section of a book and it made mention of the set of rationals not being a $G_\delta$. However, it gave no proof. I read on  about using contradiction, but it made use of the Baire category theorem, which is unfamiliar to me. I was wondering if anyone could offer me a different proof; perhaps using the fact that the complement of $G_\delta$ is $F_\sigma$.  Thanks. Citing @inbook with biblatex: how to put authors/editors before book title? I am trying to hide Authoring information, Revision information, Publishing options tabs in create/edit node for any content type. I tried different modules with no luck. Please give me suggestions how to achieve this. Thanks a lot Where does $xe^x$ solution come from when the characteristic polynomial is square? What is this electronics symbol (four triangles?) Are there cases where a period is placed inside parentheses? In which cases the period (or a comma) should be placed inside the parentheses? Why doesn't backpropagation work when you initialize all the weight the same value (say 0.5), but works fine when given random numbers?   Shouldn't the algorithm calculate the error and work from there, despite the fact that the weights are initially the same? Using ArcPy to convert .txt to shapefile with coordinate system? I tried to define my coordinate system on creating the shapefile but when I zoom to layer I don't see my features and ArcGIS crashes. I know it's not in the coordinate system I defined for it but it shows the coordinate under properties but doesn't reflect when I zoom to layer. Here is my python code:  import arcpy  newfcName ="newfc.shp"   outpath = r"C:/FLOOD/IKEJA AND KOSOFE"  # Declaration arcpy.env.overwriteOutput=True  arcpy.env.workspace= outpath  # Create new Shapefile and add FIELDS newfc = arcpy.CreateFeatureclass_management(outpath, newfcName, "Point") # get the coordinate system by describing a feature class dsc = arcpy.Describe("newfc.shp" )  coord_sys = dsc.spatialReference  try:        # run the tool    arcpy.DefineProjection_management(newfcName , coord_sys)     # print messages when the tool runs successfully    print(arcpy.GetMessages(0))  except arcpy.ExecuteError:    print(arcpy.GetMessages(2))  except Exception as ex:    print(ex.args[0])  arcpy.AddField_management(newfc, "X", "STRING", field_length = 50) arcpy.AddField_management(newfc, "Y", "STRING", field_length = 50) arcpy.AddField_management(newfc, "Z", "STRING", field_length = 50) arcpy.AddField_management(newfc, "I", "FLOAT", field_length = 50)  # Reference Cursors cursor=arcpy.da.InsertCursor(newfc, ["X", "Y", "Z", "I"])  # Read File  a = open("C:/FLOOD/IKEJA AND KOSOFE/DEM/532722.txt","r")  inputF = a.readlines()  for line in inputF:     xCoordinate, yCoordinate, zValue, iValue = line.split(" ")      newRow = (str(xCoordinate), str(yCoordinate), str(zValue), float(iValue))      cursor.insertRow(newRow)  a.close() I've been struggling with this all day today. I imagine it's not very hard, but my algebra skills are terrible. So, how can I show that if $m&gt;n$ and $a$ is a positive integer, then $$a^{2^n}+1 \mid a^{2^m}-1.$$ I just can't get a coherent picture of what I'm supposed to do. If this too (see yesterday's question) boils down to the Unique Factorization Theorem, I would be very grateful for any intuition on how to think about this! What I'm trying to understand is, to what degree does the status/rank of the University (where one completes his/her Ph.D) matter while shaping his/her career after graduation? I would like to know the weight given to one's school in both the following cases:   While applying for post-docs/faculty positions in academia While applying to industrial research labs   For instance, I've read on some forums (I can't locate the link now) that while considering prospective applications for tenure-track faculty positions, very few Universities accept a candidate who has completed his/her Ph.D from a lower ranked school having a lesser "brand" value, irrespective of the fact whether he/she has published equally original work as his/her counterpart from an Ivy league college. How much truth is in this statement? It would be really great if someone already in academia, either as a newly-accepted faculty or someone on the Faculty Hiring committee could share their experiences/statistics on this regard. I'm simply interested to know the answer, without commenting at all on whether such a practice is justifiable.  Similarly, what about recruitment to internationally acclaimed research labs (like  or ) - what importance do they place on the pedigree of a candidate's college, before taking into consideration what they published ?  I'm personally interested in answers related to the field of Computer Science (theory), but the question is applicable to any prospective grad student in any discipline in my opinion. Feel free to share your personal experiences post-Ph.D in detail, as that would give me (and future viewers of this question) about what its like to carve a career once you are out of school! We already had multiple questions about unbalanced data when using , , ,  and a number of other similar questions, what makes it a very popular topic! Unfortunately, each of the questions seems to be algorithm-specific and I didn't find any general guidelines for dealing with unbalanced data.  Quoting , dealing with unbalanced data     (...) heavily depends on the learning method. Most general purpose   approaches have one (or several) ways to deal with this.   But when exactly should we worry about unbalanced data? Which algorithms are mostly affected by it and which are able to deal with it? Which algorithms would need us to balance the data? I am aware that discussing each of the algorithms would be impossible on Q&amp;A site like this, I am rather looking for a general guidelines on when it could be a problem. What should happen if a logo I made is similar to another? In chat, the short code [metaso] expands to http://meta.stacexchange.com/ (no typo, the missing 'k' is the bug I'm reporting).  (And since this is too short a bug report, I'll note that I think that [metaso] should probably point to .) I want to select questions that are only tagged as SQL, SQLServer, SQLSever 2008. I am not interested in questions that have anything more than these tags. How do i select such questions only ? Could a Homorphus Charm Change a Werewolf Back Into a Human Before the Moon Cycle Ends? ‘Nice loud howl, Harry – exactly – and then, if you’ll believe it, I pounced – like this – slammed [the werewolf] to the floor – thus – with one hand, I managed to hold him down – with my other, I put my wand to his throat – I then screwed up my remaining strength and performed the immensely complex Homorphus Charm – he let out a piteous moan – go on, Harry – higher than that – good – the fur vanished – the fangs shrank – and he turned back into a man. Simple, yet effective – and another village will remember me forever as the hero who delivered them from the monthly terror of werewolf attacks.’   Gilderoy Lockhart - Chamber of Secrets - chapter 10 - The Rogue Bludger   Yeah, yeah. I know: consider the source! We all know Gilderoy Lockhart is a fake and a fraud in that he took credit for other heroic wizards' work. However, it occurred to me that in order to sell his books, he would have had to have written accurate and real spells and charms and potions, etc, into the books, or else everyone would have known right away that he was a turkey.   So is it possible there's an actual Homorphus Charm that will change a werewolf back into a human before the werewolf's moon cycle is over? If so, why on earth would they not have used it on Remus Lupin (for Lupin's safety) or Fenrir Greyback (for the community's safety)? Assume that $f$ be continuous on $\mathbb{R}$, $f'(x)$ exists for all $x\neq 0$, and $\lim_{x\rightarrow 0} f'(x)=1$. We need to show $f'(0)$ exist and is equal to $1$.  $f'(0)=\lim_{x\rightarrow 0}\frac{f(x)-f(0)}{x}$, $\lim_{x\rightarrow 0}f'(x)=1\Rightarrow\lim_{x\rightarrow 0}\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}=1$...am I going in the right direction? Please help. Can a satellite remain directly over a city? Is it possible to put an artificial satellite into an orbit in such a way that it will always remain direct over a city (I mean at any specific place)? Divisibility, LCM and GCD for fractions (rationals) how do i find lcm of two fractions?  For example:  $\frac{2}{3}$ and $\frac{5}{8}$