Encopresis frustration
Encopresis: how can we encourage our child to clean himself or ask for help immediately instead of ignoring the dirty underwear?
My web application generates a lot of reports in formats like excel sheet, Csv(comma-separated values), fixed width columns, pdf format, html reports etc based on the parameters I select. There is a lot of data in the reports.  Are there any essential criteria for testing report generation that I may not have considered.  I know to test these things:   Data is correct Filters are used Output format is correct   What else is there? How to get rid of notch at pgfplots axes intersection? Best Algebraic Topology book/Alternative to Allen Hatcher free book? Allen Hatcher seems impossible and this is set as the course text?  So was wondering is there a better book than this? It's pretty cheap book compared to other books on amazon and is free online.   Any good intro to Algebraic topology books?  I can find a big lists of Algebraic geometry books on here. On a very old thread on Maths overflow someone recommended that a person should read James Munkres Topology first, then you should read Allen Hatcher book.   It just seems like Rudin's book but crammed with ten times more material. How can I avoid asking duplicate questions? I posted an answer (pointing to another question already asked) but when I hit submit, I saw my answer appear as a comment to the question instead.   I tried it a couple of times and still the same result. The answer gets eaten up and is transformed into a comment.   Is this a bug? Questions on "All Horse are the Same Color" Proof by Complete Induction I'm bugged by the following that's summarized on p. 109 of .     False theorem: All horses are the same color.      Proof by induction:      $\fbox{$P(n)$ is the statement: In every set of horses of size $n$, all $n$ horses are the same color.}$   $\fbox{Base Case or $P(1)$:}$ One horse is the same color as itself. This is true by inspection.   $\fbox{Induction Step:}$ Assume $P(k)$ for some $k \geq 1$.   $\fbox{Proof of $P(k + 1) :$}$   Since $\{H_1, H_2, ... , H_n\}$ is a set of $n$ horses, the induction hypothesis applies to this set. Thus, all the horses in this set are the same color.   Since $\{H_2, H_3, ... , H_{n+1}\}$ is also a set of $n$ horses, the induction step likewise holds for this set. Thus, all the horses in this set are the same color too.         Therefore, all $n +1$ horses in $\{H_1, H_2, H_3, ... , H_n , H_{n+1}\}$ are the same color. QED.   The issue the instructor was trying to point out is clearly valid. For the case $n = 1$, there is only ${H_1}$. So this case says nothing about possible overlapping elements of each set of $(n + 1)$, for instance $H_2$ in the above proof.    But it was proposed in the class discussion that this was the only problem. Had you been able to prove $P(2)$ true, then a proof of the above format would have been fine.    My interpretation is that yes, you could prove all horses are the same color, if you can prove that any set of two horses will be the same color. But this format would not work.  Why not? The problem I see is that the above proof is for the existence of at least one particular pair of sets of horses of sizes $n$ and $n + 1$, such that in each set, all horses are the same color.  Particularly when the set of size $n$ is a subset of the set of size $n + 1$.  In order to prove the induction step, don't you need to prove that sets of sizes $n$ and $n + 1$, do not necessarily contain the same, overlapping elements?  You could prove that any horse can be added to a set of 2 horses.  Take the last two, and they must be the same color, and so on.  Wwhatever color the first two happen to be, all other horses must thus be the same color.    Am I misinterpreting the example, or am I making a logical error? Thanks in advance. Eigenvectors of real symmetric matrices are orthogonal Can someone point me to a paper, or show here, why symmetric matrices have orthogonal eigenvectors? In particular, I'd like to see proof that for a symmetric matrix $A$ there exists decomposition $A = Q\Lambda Q^{-1} = Q\Lambda Q^{T}$ where $\Lambda$ is diagonal. Is it bad practice to return from within a try catch finally block? So I came across some code this morning that looked like this:  try {     x = SomeThingDangerous();     return x; } catch (Exception ex) {     throw new DangerousException(ex); } finally {     CleanUpDangerousStuff(); }   Now this code compiles fine and works as it should, but it just doesn't feel right to return from within a try block, especially if there's an associated finally.  My main issue is what happens if the finally throws an exception of it's own? You've got a returned variable but also an exception to deal with... so I'm interested to know what others think about returning from within a try block? I am looking for a proof possibly using the sandwich theorem and/or Bernoulli's inequality for proving the following statement:  If $x&gt;0$ then $x^{1/n}$ tends to $1$. I recently updated my profile bio (from Arqade) and clicked 'Save and copy changes to all public communities'. This appears to have broken/reset my profile picture on all but Arqade. Note that I did not update my profile picture as part of my changes. Arqade:  Meta SE for comparison:  I haven't touched my profile picture in years. Is this a bug?  Update: It appears my profile pic across all communities has been set back to 'Identicon'. I went on to Stack Overflow and changed my profile picture back to 'Gravitar' and clicked 'Save and copy to all communities' again, but this did not update my profile picture anywhere but SO. (I did the same on Sustainability to be doubly sure). Update 2: This is a persistent bug - I had changed most of my SE communities back to my 'Robotnik' display pic over the past little while. Today I edited my profile again on Arqade, Clicked 'Save and copy' - and the display pic reverted back to identicon again across all sites. Update 3: I have re-uploaded my profile picture and the 'Save and copy' function worked. It appears that this is actually a bug to do with the old images from Gravatar. Problem from Herstein on group theory The problem is:  If $G$ is a finite group with order not divisible by 3, and $(ab)^3=a^3b^3$ for all $a,b\in G$, then show that $G$ is abelian.  I have been trying this for a long time but not been able to make any progress. The only thing that I can think of is: $$ab\cdot ab\cdot ab=aaa\cdot bbb\implies(ba)^2=a^2b^2=aabb=(\text{TPT})abba.$$ Now, how can I prove the last equality? If I write $aabb=abb^{-1}abb$, then in order for the hypothesis to be correct, $b^{-1}abb=ba\implies ab^2=b^2a$. Where am I going wrong? What should I do? Claim: Let $X$ be a metric space. If $A,B\in X$ are disjoint, if A is compact, and if B is closed, then $\exists \delta&gt;0: |\alpha-\beta|\geq\delta\;\;\;\forall\alpha\in A,\beta\in B$.  Proof. Assume the contrary. Let $\alpha_n\in A,\beta_n\in B$ be chosen such that $|\alpha_n-\beta_n|\rightarrow0$ as $n\rightarrow \infty$.  Since A is compact, there exists a convergent subsequence of $\alpha_n\;(n\in\mathbb{N})$, $\alpha_{n_m}\;(m\in\mathbb{N})$, which converges to $\alpha\in A$.  We have   $$|\alpha-\beta_{n_m}|\leq|\alpha-\alpha_{n_m}|+|\alpha_{n_m}-\beta_{n_m}|\rightarrow0 \;\;\;as\;\;m\rightarrow\infty.$$ Hence $\alpha$ is a limit point of B and since B is closed $\alpha\in B$, contradiction.  Is my proof correct? I feel as though I am missing something simple which would trivialize the proof. How do I write to NTFS drives in OS X? I work sometimes till 4 am and my friends and the rest of the world obviously don't know in advance that I don't want to be called at 8 am.  Is there an app or setting that can allow me to have an emergency override list of people I need to be woken up for if a possible emergency arises but ignore all other calls until I wake up?    I'm familiar with the Do Not Disturb option, but it has limitations that it blocks all calls. What if there is an emergency at night?  What if I want to allow certain callers during the Do not Disturb time? Is there a way to have an emergency list that allows calls during silent? How can I view the contents of tar.gz file without extracting from the command-line? I want to see the contents (list of files and folders) of an archive, for example a  tar.gz file without extracting it.  Are there any methods for doing that? I saw  hosted by Stephen Hawkins.  And if I didn't get it wrong, it says that there was no time before the big bang, time was created there.  So how can anything happen when there is no time (eg: the creation of time and the universe)? Is this what he calls a 'singularity'? Which I could think like this: when there is no time nothing can happen, except during this singularity.  Of course I don't know of a law that says 'when there is no time nothing can happen..', I just came up with it, as something intuitive. How can I reuse existing materials, objects, etc from an existing .blend? How can I customize a system locale? What does % do to strings in Python? Adding words to links generated by hyperref \documentclass{article} \usepackage{hyperref} \usepackage{lipsum} \usepackage{polski} \begin{document} \begin{figure} . \caption{A figure} \label{fff} \end{figure} \lipsum[1]  Rysunek~\ref{fff} jest zabawny, bo na rysunku~\ref{fff} nic nie ma. \end{document}   In this sample, a clickable link is added to output PDF for 1 and 1. I want to be able to change them to Rysunek 1 and rysunku 1. I want to be able to put any other text + number of the figure into a hyperlink. The word rysunek can't be set in preamble as a default because there is a declension in Polish. The same question goes for tables, listings, equations, pages (pageref) etc (basically any reference).  HTML equivalent of my MWE:    Rysunek &lt;href="fff"&gt;1&lt;/a&gt; jest zabawny, bo na rysunku &lt;a href="fff"&gt;1&lt;/a&gt; nic nie ma.   I want it to be:    &lt;href="fff"&gt;Rysunek 1&lt;/a&gt; jest zabawny, bo na &lt;a href="fff"&gt;rysunku 1&lt;/a&gt; nic nie ma.