I'm actually writing a scientific article, and my professor is correcting all my (numerous) grammar errors.  One in particular is bugging me. In my article I wrote     "[object] that lets us introduce [object]"   and was corrected into     "[object] that lets us  to introduce [object]"   My form is totally wrong? Or are they both correct? And why?    As  shows, the base rule imposes to not use the "to". My question here is a bit more specific.  Is the expression used above indicated/correct for a formal/scientific document?
I let him do it.   and     I allow him to do it.   Why does the latter require to?  What are the "rules" of using to with an infinitive? When is it necessary?
Why is Excel truncating my 16-digit numbers? If I type in a 16 digit number (format: number, no decimals) it changes the number on me. Example: 1234567812345678 changes the view to 1234567812345670.    If I type it in as a general format it changes the numbers above so it displays 1.23457E+15 but if you click on the cell, the display shows the last digit as a 0 instead of an 8 once again.   I opened the file on a different computer and same issue now with it.  I have changed the auto correction and auto formatting all to no avail.  Help! In which cases should I use the subjunctive mood?     I suggest that every applicant fill out the form carefully.        If she were rich, she would live on Long Island. Include the "People Reached" and "Helpful Flags (count)" data in SEDE What happens to the semiconductor in an LED when it is given voltage that it cannot handle? Using 'return' instead of 'else' in JavaScript Is the trace of inverse matrix convex? Using k-fold cross-validation for time-series model selection Question: I want to be sure of something, is the use of k-fold cross-validation with time series is straightforward, or does one need to pay special attention before using it?   Background: I'm modeling a time series of 6 year (with semi-markov chain), with a data sample every 5 min. To compare several models, I'm using a 6-fold cross-validation by separating the data in 6 year, so my training sets (to calculate the parameters) have a length of 5 years, and the test sets have a length of 1 year. I'm not taking into account the time order, so my different sets are :   fold 1 : training [1 2 3 4 5], test [6] fold 2 : training [1 2 3 4 6], test [5] fold 3 : training [1 2 3 5 6], test [4] fold 4 : training [1 2 4 5 6], test [3] fold 5 : training [1 3 4 5 6], test [2] fold 6 : training [2 3 4 5 6], test [1].   I'm making the hypothesis that each year are independent from each other. How can I verify that? Is there any reference showing the applicability of k-fold cross-validation with time series. Prove that there exists irrational numbers $x$ and $y$ such that $x + y$ is rational, without using subtraction My homework has this problem:     Prove that there exist irrational numbers $x$ and $y$ such that $x +  y$ is rational.   There is an easy solution that I found on mathbitsnotebook.com:     \begin{align} \left(2+6\sqrt{7}\right) + \left(-6\sqrt{7}\right) = 2.\end{align}   Can we prove the same without using subtraction? What is the most ruby-ish way of accessing nested hash values at arbitrary depths? Minimal cut edges number in connected Eulerian graph. I have to prove that Connected graph is Eulerian Graph if and only if the number of edges in minimal cut is even.  Implication from left to right. Well if $G$ is Eulerian Graph then degree of each vertex must be even. It's oblivious if i try to disconnect graph by removing all edges connected to the vertex with minimal degree. But minimal cut can be done also by dividing graph into 2 connected graphs (each graph with more then one vertex) and i have no idea how to deal with it.  Implication from right to left - completly no idea. CSS Display an Image Resized and Cropped I want to show an image from an URL with a certain width and height even if it has a different size ratio.  So I want to resize (maintaining the ratio) and then cut the image to the size I want.  I can resize with html img property and I can cut with background-image.  How can I do both?  Example:  This image:     Has the size 800x600 pixels and I want to show like an image of 200x100 pixels   With img I can resize the image 200x150px:  &lt;img      style="width: 200px; height: 150px;"      src="http://i.stack.imgur.com/wPh0S.jpg"&gt;    That gives me this:    &lt;img style="width: 200px; height: 150px;" src="https://i.stack.imgur.com/wPh0S.jpg"&gt;       And with background-image I can cut the image 200x100 pixels.  &lt;div      style="background-image:            url('https://i.stack.imgur.com/wPh0S.jpg');      width:200px;      height:100px;      background-position:center;"&gt;&amp;nbsp;&lt;/div&gt;    Gives me:        &lt;div style="background-image:url('https://i.stack.imgur.com/wPh0S.jpg'); width:200px; height:100px; background-position:center;"&gt;&amp;nbsp;&lt;/div&gt;      How can I do both?  Resize the image and then cut it the size I want? Let $a_n=\sqrt[n]n-1$. Does $\sum_{n=1}^\infty a_n$ converge? Where's the problem in this equation? Resulting in $4 = 5$ I just saw this equation and I can't find out where's the problem:  $$25-45 = 16-36$$  $$25- 2 \cdot 5 \cdot \frac{9}{2} = 16- 2\cdot4\cdot\frac{9}{2}$$  $$25 - 2\cdot 5\cdot \frac{9}{2} + \frac{81}{4} = 16 - 2\cdot 4 \cdot \frac{9}{2} + \frac{81}{4}$$  $$\left( 5-\frac{9}{2} \right) ^2 = \left (4-\frac{9}{2} \right) ^2$$  $$5-\frac{9}{2} = 4 - \frac{9}{2}$$ $$5=4$$ $(x^3+xy^2-y)dx+(y^3+x^2y+x)dy=0$ I tried to find on Wolfram Alpha but it showed only the solution not in step-by-step, I know that the factor is $\frac{1}{x^2+y^2}$ but how to find it? Why the Galaxy has 25GB instead of 32GB I just purchased a Samsung Galaxy S3 32GB, when I check the storage I have only 25.5GB. Where is the other 6.5GB? When should I use \input vs. \include? There are two different commands to incorporate another file into the source of some document, \input and \include. When should I use one or the other? What are the differences between them? Are there more things like them to be aware of? "Has/Have/Had" as a main verb and auxiliary verb I need help regarding the use of has/have/had both as a main verb and as an auxiliary verb.  In the sentence below, the word has acts as the main verb. I would normally follow it with the phrase "so do I."        Kenny has a car, and so do I.      On the other hand, the word has in the following sentence acts as an auxiliary verb. I would normally follow it with the phrase "so have I."        Kenny has bought a car, and so have I.      a) Are sentences 1 &amp; 2 above correct? I'm under the impression that so do I is used when has/have/had is the main verb of a sentence, and so have/had I if it's an auxiliary verb in a sentence.  b) Does the verb has/have always need a supporting "auxiliary verb" (either implied or mentioned)? (e.g., Kenny has a car = Kenny does have a car.) Where is the right place to register/enqueue scripts & styles I am using WordPress 3.1.4 by now. I am confused with where (which hook) do I use:   to register and/or enqueue  scripts and styles  on front- and back-ends?   Questions:   Which are right hooks to use? All front end register/enqueue scripts/styles in init? Why is there no admin_print_styles-{xxx}? Idea behind proof that $\frac{21n+4}{14n+3}$ is irreducible for all $n$ I have a proof of $\frac{21n+4}{14n+3}$ being an irreducible fraction for any positive integer $n$. The proof starts with the following: Indeed, from the equality: $$2(21n+4)-3(14n+3)=-1$$ and so on..But how does this equality follow from the fraction? Ignore compile errors How can I set up a permanent compile loop that keeps trying even when there are errors? I'm using latexmk with a remote compile setup as discussed  and . However, if I save a document with a bug (either a legitimate bug, or I save it before closing a tag), then latexmk halts. Any suggests how I can have it pause, try again, and keep trying again, for ever and ever?