A limit of a sequence
Prove that $\lim \limits_{n \to \infty} \frac{x^n}{n!} = 0$, $x \in \Bbb R$.
Where to place log4j.xml How do I get the path and name of the file that is currently executing? Network reputation graph becomes nervous when clicking quickly, backs away slowly Let's consider two statements: Zorn's lemma and theorem about existence of maximal ideals in commutative ring with $1$.  It's easy to prove that Zorn's lemma implies existence of maximal ideals.  I wonder if the converse proposition is true, i. e., does existence of maximal ideals implies Zorn's lemma? My approach was to construct a ring structure on an ordered set which satisfies Zorn's lemma condition such that existence of maximal ideal implies existence of maximal element in the set, but I didn't succeed. Get referenced node fields in twig Encode multi-class response variable In a classification problem when the response variable has multi-class, e.g., "sunny","rainy","cloudy", how should we encode it? I know that for predictors like this, usually we do , and if a predictors have too many classes, then we might just use the .   When this multi-class issue occurs in the response variable, I guess we can just use LabelEncode() rather use using One Hot encoding right? Because if we use One Hot encoding, then we will have 2 variables as the response variable, and the machine learning algorithm in sklearn usually expects the response variable not to be a vector right? (I mean it expects a long 1D vector with length equal to the number of observations but not a 2D matrix). But on the other hand, if we just map "sunny", "rainy","cloudy" to {1,2,3} or {0,1,2}, or whatever 3 numbers, that will create a less than or greater than relationship among "sunny", "rainy","cloudy", which is not inherited in the original problem. Convert one date format into another in PHP how to disable system apps without root? How can I install the Google Apps Package (Play Store, ...) on my Android device? 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Restricted logins with automatic full permission in databases My scenario: I have some groups with full - and inappropriate - access to all Sql Server instances. I want to change that.  My Plan: Give full and automatic access to all databases (it is customer databases and this groups must be allowed to change any property if necessary).  Restrict permissions on Instance Level, because this groups should not be allowed to do any unexpected change on instance properties.  I don't want to create a user in databases, because our external customer could drop the user ( they have db_owner permission )  Someone have any idea? Tks Creating random numbers with no duplicates Does existence of $\gcd$ implies PID? Without appealing to the axiom of choice, it can be shown that (Proposition:) if $X$ is well-orderable, then $2^X$ is totally-orderable.  Question: can we show the stronger result that if $X$ is well-orderable, then so too is $2^X$?  Proof of Proposition. Pick any well-ordering of $X$. 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