say we have a fixed table T. Is there a unique normalized version of T, i.e., does the/a correct normalization, say up to 3NF produce a unique table up to some equivalence? Basically, I am trying to find out how many different correct ways of normalizing a table there are. Thanks.
I"m studying normalization and have been reading through descriptions and examples online. One Concept that isn't clear to me is if the process can be automated at any point. I understand that a system can't tell you if you schema makes any real-world sense, but it seems likely to me that if you feed a program some arguments say, the functional dependencies, it would be able to do some steps for you.  Say you have a relationship R(A,B,C,D)  and you tell your program that A,B->C and A->D and that the primary key is (A,B)  Now if my understanding serves me correctly it should be possible for a program to identify that A->D violates 2NF because D depends on A and A is a subset of the primary key. That the proper decomposition would be R1(A,B,C) and R2(A,D).   The main book i'm learning from and my instructor indicate these normalization's are done all by hand. Is this correct or can some parts be automated?
What causes the expansion of space? Get Site Collection full URL using javascript I have read in a book that the limit of the ratio of consequent Fibonacci numbers is the golden ratio. However, it was just mentioned thus not justified. So, my question is how would you derive the following limit: $$\lim_{x\to\infty}{\frac{F_n}{F_{n+1}}}=?$$ Where $F_n$ is the nth Fibonacci number? Installing TTF fonts in LaTeX One of the annoying aspects of LaTeX is the limited number of fonts that come by default, and the pain involved in making new fonts 'LaTeX' ready. I have a collection of truetype fonts that I'd like to prepare for use, and I definitely want to make sure I have vector versions of these fonts (i.e not type 3/bitmapped versions). Is there a relatively painless way to do this ? Can anybody explain the UNABLE_TO_LOCK_ROW error? Error Message:     Developer script exception from Nicomatic : quotepotential :   quotepotential: execution of AfterUpdate caused by:   System.DmlException: Update failed. First exception on row 0 with id   a0Q90000005PoxtEAC; first error: UNABLE_TO_LOCK_ROW, unable to obtain   exclusive access to this record: [] Trigger.quotepotential: line 14,   column 1      Apex script unhandled trigger exception by user/organization:   00590000001A6jh/00D90000000bovq      quotepotential: execution of AfterUpdate      caused by: System.DmlException: Update failed. First exception on row   0 with id a0Q90000005PoxtEAC; first error: UNABLE_TO_LOCK_ROW, unable   to obtain exclusive access to this record: []      Trigger.quotepotential: line 14, column 1   these mails are getting to my mail..........  trigger quotepotential on Quote_Line_Item__c (after insert,after update) {     Set&lt;Id&gt; quoteIds = new Set&lt;Id&gt;();     List&lt;Quote__c&gt; quotes = new List&lt;Quote__c&gt;();     for (Quote_Line_Item__c record: Trigger.new) {         if (record.Quote1__c != null){             quoteIds.add(record.Quote1__c);         }     }     for(AggregateResult ar:[                 SELECT                      Quote1__c,                      SUM(Max_Batch__c)sumMax                  FROM Quote_Line_Item__c                  WHERE Quote1__c=:quoteIds                  GROUP BY Quote1__c                 ]) {          quotes.add(new Quote__c(              Id=(Id) ar.get('Quote1__c'),              Potential__c = (Decimal) ar.get('sumMax')              ));     }     if (quotes.isempty() == false) {         update quotes;     } } Why is $\frac{1}{\frac{1}{0}}$ undefined? Infinite sum of ideals I've been trying to prove that given a ring $R$ and a collection of ideals $\{I_{\beta}\}_{\beta \in B}$ in $R$, the set $$\sum_{\beta \in B} I_{\beta}=\{f_1+\cdots+f_r:f_j \in I_{\beta_j}, \mbox{ for some } I_{\beta_j}\}$$ is an ideal and is the smallest ideal containing $\cup_{\beta \in B} I_{\beta}$.  I've already proved when I only have two ideals, and so, using induction, I've seen it for finite sums. But I don't see how to generalise that to an arbitrary family of indexes (maybe infinite) $\beta$.   Could someone please give me a hand? Thank you. Why does Yoda speak the way he does? automatically execute an Excel macro on a cell change Why don't the Ubuntu repositories have the latest versions of software? Using customized Coordinate System in ArcGIS Desktop? Why is the light reflected at the same angle from mirror? From the school physics I know that the material objects bounce from the plane surface at the same angle, losing some kinetic energy. In the same school I was taught that the light (and waves in general) obeys this principle too.  Obviously, in the case of light the plane surface should be a perfect mirror. But I can't understand how should this work from the quantum point of view. Let's assume that our mirror consists of a single silver atom.  Why should the electrons of this atom re-emit consumed photons at some specific angle? How unusual is getting a Masters degree in a slightly different field than Bachelors? Would it be out of the ordinary to get a Bachelors in Mechanical Engineering and then go for a Masters in something like Civil or Structural Engineering?  I don't know a lot about how transitioning to a Masters program works.. Do people usually continue on in the same field, or is branching out common? I tried getting a good measurement with my caliper, but the flexibility of the tire doesn't help much. Let's say I have a 26&quot;x2.125&quot; tire. I know this fits on an ISO 559mm bead seat diameter rim, and 26&quot; = 660.4mm. 26&quot;:  The OD of the tire including the tread? The OD of the tire excluding the tread? When aired up or deflated? Means it fits a 559mm ISO BSD None of the above?  2.125&quot;:  Width of tread? Width of sidewall? Inflated or deflated?  Essentially, I'm converting the tire sizes to &quot;height off rim in mm&quot; and drawing them with a wheel in a web application, so I need to know how &quot;tire size&quot; translates to this measurement. I'm somewhat assuming that the fractional sizes can be converted to the same measurement, but I'm aware that they have certain differences - so any help there would be of value as well.  has been helpful, but still leaves me with the questions above. $H$ is normal subgroup of $G$ iff $gHg^{-1}=H$ for every $g$ of $G$ Given the following definition of normal subgroup     A subgroup $H$ of a group $G$ is said to be normal if, for every $g\in G$: $$gH=Hg$$   I've tried to show that $H\mathrel{\unlhd} G$ if and only if we have $gHg^{-1}=H$ for every $g\in G$:  (if) Let $H\mathrel{\unlhd} G$, $g\in G$; if $l\in gHg^{-1}$, there exists $h\in H$ such that $l=ghg^{-1}$ and since $gh$ = $h'g$ for some $h'\in H$, then $l=ghg^{-1}=h'(gg^{-1}) = h'\in H$. Let $h\in H$; we can write $h$ as $hgg^{-1}$, and since $hg = gh'$ for some $h'\in H$, we obtain $h = hgg^{-1} = gh'g^{-1}\in ghg^{-1}$. So $gHg^{-1}=H$.  (only if) Let $gHg^{-1}=H$, $g\in G$; if we take an $l\in Hg$, $l = hg$ for some $h\in H$, we note immediately that $l=hg=(gh'g^{-1})g=gh'\in gH$. What should I do to show that $gH\subset Hg$?  I'm also wondering if this mess is correct, and if it is possible a more elegant proof of this fact. I need a list of integers from 1 to x where x is set by the user.  I could build it with a for loop eg assuming x is an integer set previously:  List&lt;int&gt; iList = new List&lt;int&gt;(); for (int i = 1; i &lt;= x; i++) {     iList.Add(i); }   This seems dumb, surely there's a more elegant way to do this, something like the I feel that I might have a complete misunderstanding here. If DNA has two strands, how does the machinery of RNA transcription determine which one to transcribe? Academic rank equivalence between the UK and the US systems How to do a secure erase on a Macbook Pro? I have a Macbook Pro with SSD and I would like to completely erase every single bits of data on it. How would I do that? On a PC, I would just run Darik's Boot And Nuke, but can I run it on a Mac too, or is there a better alternative? Is there any hint of of the first Wizarding War being an international event? Is there any hint that the MoM or anywhere else got support in combating voldemort the first time around? Or is everything completely UK-centric?  I can't remember anyone in the second war being specifically sent from europe to help, even though we see international wizards in book 4. But I don't think all the events of the first war are covered in the books.  So are other bodies like the MoM involved in the first war, or was it isolated in the UK?