It's a nice book but it's 'too' expensive. I'm not going to buy it. I would buy it if it weren't 'so' expensive.   These are from the book 'English Grammar in Use'.  So, I'm sure that these are the perfect sentences. However, is it okay to use 'so' rather than 'too' in the first sentence and 'too' rather than 'so' in the second one?
I have a problem with using "too" in a sentence. In what situation would you use "too" instead of "so" or "very"? Please include an example to illustrate the difference.
Show that if $f(z)$ is an entire function such that it takes real values on the lines $Im(z)=0$ and $Im(z)=a$ (for some $a \in \mathbb{R}_{\neq 0})$, then $f$ is periodic with period $2 i a$.    So here is my thought process: First of all by reflection principle $f(\bar{z})=\overline{f(z)}$ so if our function $f$ is given in the strip $0 \leq Im(z) \leq a$, then its values on $-a \leq Im(z) \leq a$ follow by reflection principle. Then by imposing $f(z)=f(z+2 ia)$ we can intuitively see that this will define an entire function by looking at how the strips $na \leq Im(z) \leq 2na$ seamlessly stack on top of each other. Is this logical? And how would one prove this analytically? Derivation of Maxwell's equations from field tensor lagrangian I've started reading Peskin and Schroeder on my own time, and I'm a bit confused about how to obtain Maxwell's equations from the (source-free) lagrangian density $L = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}$ (where $F^{\mu\nu} = \partial^\mu A^\nu - \partial^\nu A^\mu$ is the field tensor).  Substituting in for the definition of the field tensor yields $L = -\frac{1}{2}[(\partial_\mu A_\nu)(\partial^\mu A^\nu) - (\partial_\mu A_\nu)(\partial^\nu A^\mu)]$.  I know I should be using $A^\mu$ as the dynamical variable in the Euler-Lagrange equations, which become $\frac{\partial L}{\partial A_\mu} - \partial_\mu\frac{\partial L}{\partial(\partial_\mu A_\nu)} = - \partial_\mu\frac{\partial L}{\partial(\partial_\mu A_\nu)}$, but I'm confused about how to proceed from here.  I know I should end up with $\partial_\mu F^{\mu\nu} = 0$, but I don't quite see why.  Since $\mu$ and $\nu$ are dummy indices, I should be able to change them: how do the indices in the lagrangian relate to the indices in the derivatives in the Euler-Lagrange equations? Let $G$ be a finite semi-group with identity such that it has only one idempotent.Is $G$ a group?  It only remains to show that for any $a\in G$ $\exists b\in G$ such that $ab=ba=e$ where $e$ is the identity of $G$  Also $e$ is the only idempotent of $G$ .How to proceed next? For some reasons, I would like to do an explicit quoting of a string value (becoming a part of constructed SQL query) instead of waiting for implicit quotation performed by cursor.execute method on contents of its second parameter.  By "implicit quotation" I mean:  value = "Unsafe string" query = "SELECT * FROM some_table WHERE some_char_field = %s;" cursor.execute( query, (value,) ) # value will be correctly quoted   I would prefer something like that:  value = "Unsafe string" query = "SELECT * FROM some_table WHERE some_char_field = %s;" % \     READY_TO_USE_QUOTING_FUNCTION(value) cursor.execute( query ) # value will be correctly quoted, too   Is such low level READY_TO_USE_QUOTING_FUNCTION expected by Python DB API specification (I couldn't find such functionality in  document). If not, maybe Psycopg2 provides such function? If not, maybe Django provides such function? I would prefer not to write such function myself... If $\frac{\sin^4 x}{a}+\frac{\cos^4 x}{b}=\frac{1}{a+b}$, then show that $\frac{\sin^6 x}{a^2}+\frac{\cos^6 x}{b^2}=\frac{1}{(a+b)^2}$ If $\frac{\sin^4 x}{a}+\frac{\cos^4 x}{b}=\frac{1}{a+b}$, then show that $\frac{\sin^6 x}{a^2}+\frac{\cos^6 x}{b^2}=\frac{1}{(a+b)^2}$     My work: $(\frac{\sin^4 x}{a}+\frac{\cos^4 x}{b})=\frac{1}{a+b}$ By squaring both sides, we get, $\frac{\sin^8 x}{a^2}+\frac{\cos^8 x}{b^2}+2\frac{\sin^4 x \cos^4 x}{ab}=\frac{1}{(a+b)^2}$ $\frac{\sin^6 x}{a^2}+\frac{\cos^6 x}{b^2}-2\frac{\sin^4 x \cos^4 x}{ab}-\frac{\sin^6 x \cos^2 x}{a^2}-\frac{\sin^2 x \cos^6 x}{b^2}=\frac{1}{(a+b)^2}$ So, now, we have to prove that, $-2\frac{\sin^4 x \cos^4 x}{ab}-\frac{\sin^6 x \cos^2 x}{a^2}-\frac{\sin^2 x \cos^6 x}{b^2}=0$ I cannot do this. Please help! Android OS without Google Services? MySQL: "UPDATE command denied to user ''@'localhost'" Replacing fonts in EPS/PDF files I'm looking to clarify the differences/overlaps between the three and, if the terminology isn't accurate establish the correct terminology Which PHP function can return the current date/time? Parsing domain from a URL List selectors for Objective-C object I have an object, and I want to list all the selectors to which it responds. It feels like this should be perfectly possible, but I'm having trouble finding the APIs. Using Windows DLL from Linux This is my follow up question. My previous question is here:   Problem:  If I add the image in my table, I get the following output as shown in the image below. Why is the Co-Supervisor going below?   I am using this code:  \begin{tabular}{|l|c|r|} \hline \bf Author: &amp; \hspace{5pt} &amp; \bf Research Supervisor:\\ \hline Mr. X &amp;  \hspace{5pt} &amp; Prof. Dr. Z\\ \hline \includegraphics[width=0.40\textwidth,height=10mm]{Figures/images} &amp;  \hspace{5pt} &amp; \bf Co-Supervisor:\\ \hline &amp;  \hspace{5pt} &amp; Prof. Dr. Y\\ \hline \end{tabular}   What I want is shown below:   PS: Please ignore the table borders, they are for demo only, I won't be using them in my final code.  The final product: that I desire is: What is the correct way of installing BOINC software? Finding centrelines from polygons in QGIS? I was wondering if there is a way to create centre lines from polygons in QGIS? I have a polygon layer, but ideally need the centrelines as a separate file. Prove $\sum_{d \leq x} \mu(d)\left\lfloor \frac xd \right\rfloor = 1 $ Is GTA Online cross-platform? I am trying to display certain features in a shapefile-based layer using QGIS. I have found the subset function in the properties panel, which does exactly what i want, but is too tedious given that I have to manually sift through a large number of features. Is there a quicker way to do this?  I am using both shapefiles and postGIS best,  dietmar Can anyone tell me how to judge if a supervised machine learning model is overfitting or not? If I don't have an external validation dataset, I want to know if I can use ROC of 10 fold cross validation to explain overfitting. If I have an external validation dataset, what should I do next?