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How to fix pagination for custom loops? I have added a custom/secondary query to a template file/custom page template; how can I make WordPress use my custom query for pagination, instead of using the main query loop's pagination?  Addendum  I have modified the main loop query via . Why isn't pagination working, and how do I fix it? Most textbooks introduce differentiable manifolds via . This has the advantage of being concrete, but the disadvantage that the local coordinates are usually completely irrelevant- the choice of atlas and chart is arbitrary, and rarely if ever seems to play any role in differential geometry/topology.  There is a much better definition of differentiable manifolds, which I don't know a good textbook reference for, via . This definition does not involve any strange arbitrary choices, and is coordinate free. Paragraph 3 in Wikipedia (which is the actual definition) states:   A differentiable manifold (of class $C_k$) consists of a pair $(M, \mathcal{O}_M)$ where $M$ is a topological space, and $\mathcal{O}_M$ is a sheaf of local $R$-algebras defined on $M$, such that the locally ringed space $(M,\mathcal{O}_M)$ is locally isomorphic to $(\mathbb{R}^n, \mathcal{O})$.   This confuses me, because I don't see why such a sheaf should be acyclic, or where conditions like "paracompact" or "complete metric space" or "second countable Hausdorff" are implicit. So either:   The wikipedia entry has a mistake (I would want to sanity-check this before editing the entry, because this is such a fundamental definition which thousands must have read). Somewhere in that definition, the condition that $M$ be paracompact is implicit.   Question: Should the definition above indeed require that $M$ be second-countable Hausdorff or paracompact or whatever? Or is it somehow implicit somewhere, and if so, where?    Also, is this definition given carefully in any textbook?  Update: I have editted the Wikipedia article to require that $M$ be second-countable Hausdorff. But I'm still wondering if there is a textbook covering this stuff, and whether requiring the sheaf to be acyclic might have worked instead as an alternative. Expansion of $(1+px+qx^2)^8\equiv 1+8x+52x^2+kx^3$... $(1+px+qx^2)^8 \equiv  1+8x+52x^2+kx^3...$  Given that expression, calculate the values of p, q, and k.  I'm guessing this is a trinomial that needs to be turned into a binomial, but how would you do it? I have no idea. "Cannot find this file" error when deploying from Visual Studio 2010 I'm getting an error in Visual Studio 2010 after pressing F5 to Debug:     Error occurred in deployment step 'Add   Solution': Error: Cannot find this   file specified in the manifest file:   G2_SiteDefinition_List_Instances_Feature\ListInstance1\Elements.xml   But elements.xml file is there with the ListIntance1 folder. What am I missing here? Can we clarify to the OP that their question is not yet closed and the duplicates are only suggestions? Do harmonic numbers have a “closed-form” expression? What are the differences between vector graphics and raster graphics? This is problem #6 from Section 1.2 of Ash's Real Variables With Basic Metric Space Topology.   I am asked to show that it is impossible to list the rational numbers in increasing order.   While I know it is possible to list a finite subset of the rational numbers in increasing order, I was wondering if the reason for the impossibility in this case is because there is no least element of $\mathbb{Q}$?   I mean, it's possible to impose an ordering on $\mathbb{Q}$ (correct me if I'm wrong, but it seems possible to compare any two rationals).  But the set $\mathbb{Q}$ is of course, a subset of itself, and the Well-Ordering Principle says that a set $S$ is Well-Ordered only if any subset of $S$ contains a minimal element. Since $\mathbb{Q}$ does not contain a minimal element, it does not appear that it is a Well-Ordered set.   Is this the correct idea as to why it's impossible? If not, could somebody explain to me what the correct idea is and a strategy for proving it?  Thank you ahead of time. The mystery of the tagged answer - and more It is (currently)   to tag answers. Yet, if I query , then  does have a tag, namely javascript. I'm at a loss: how did that happen?&dagger;  SELECT Id, Tag FROM Posts, PostsTags  WHERE Posts.PostTypeId = 2 AND Posts.Id = PostsTags.PostId   Edit: The are also five answers (, , ,  and ) with a view count of 1 instead of 0:  SELECT Id, ViewCount FROM Posts WHERE PostTypeId = 2 AND ViewCount &lt;&gt; 0   These results also hold through at least January 10.    &nbsp; &dagger;: PostTypeId = 2 means that the post is an answer, not a question (PostTypeId = 1). When a person lifts a book while standing on the earth's surface. Why is his force considered external to the book-earth system? Isn't his force internal like the case of the forces that cause the exploson of a bomb. I think the forces the person exerts on both the book and the earth are internal since they are equal but opposite therefore resulting in the position of the centre of mass of the system being maintained and if i'm right is the mechanical energy of the system constant?  Am i wrong? Please correct me. Inverse of function is continuous or not? Why does ice melting not change the water level in a container? I have read the explanation for this in several textbooks, but I am struggling to understand it via Archimedes' principle. If someone can clarify with a diagram or something so I can understand or a clear equation explanation that would be great. Removing control chars (including console codes / colours) from script output I can use the "script" command to record an interactive session at the command line.  However, this includes all control characters and colour codes.  I can remove control characters (like backspace) with "col -b", but I can't find a simple way to remove the colour codes.  Note that I want to use the command line in the normal way, so don't want to disable colours there - I just want to remove them from the script output.  Also, I know can play around and try find a regexp to fix things up, but I am hoping there is a simpler (and more reliable - what if there's a code I don't know about when I develop the regexp?) solution.  To show the problem:   spl62 tmp: script Script started, file is typescript spl62 lepl: ls add-licence.sed  build-example.sh  commit-test         push-docs.sh add-licence.sh   build.sh          delete-licence.sed  setup.py asn              build-test.sh     delete-licence.sh   src build-doc.sh     clean             doc-src             test.ini spl62 lepl: exit Script done, file is typescript spl62 tmp: cat -v typescript Script started on Thu 09 Jun 2011 09:47:27 AM CLT spl62 lepl: ls^M ^[[0m^[[00madd-licence.sed^[[0m  ^[[00;32mbuild-example.sh^[[0m  ^[[00mcommit-test^[[0m         ^[[00;32mpush-docs.sh^[[0m^M ^[[00;32madd-licence.sh^[[0m   ^[[00;32mbuild.sh^[[0m          ^[[00mdelete-licence.sed^[[0m  ^[[00msetup.py^[[0m^M ^[[01;34masn^[[0m              ^[[00;32mbuild-test.sh^[[0m     ^[[00;32mdelete-licence.sh^[[0m   ^[[01;34msrc^[[0m^M ^[[00;32mbuild-doc.sh^[[0m     ^[[00;32mclean^[[0m             ^[[01;34mdoc-src^[[0m             ^[[00mtest.ini^[[0m^M spl62 lepl: exit^M  Script done on Thu 09 Jun 2011 09:47:29 AM CLT spl62 tmp: col -b &lt; typescript  Script started on Thu 09 Jun 2011 09:47:27 AM CLT spl62 lepl: ls 0m00madd-licence.sed0m  00;32mbuild-example.sh0m  00mcommit-test0m         00;32mpush-docs.sh0m 00;32madd-licence.sh0m   00;32mbuild.sh0m          00mdelete-licence.sed0m  00msetup.py0m 01;34masn0m              00;32mbuild-test.sh0m     00;32mdelete-licence.sh0m   01;34msrc0m 00;32mbuild-doc.sh0m     00;32mclean0m             01;34mdoc-src0m             00mtest.ini0m spl62 lepl: exit  Script done on Thu 09 Jun 2011 09:47:29 AM CLT Test of whole distribution for two samples Why would I buy a bond with a negative yield? The only reason that I can think of is because I expect the bond to appreciate in price thus offsetting the loss in yield. I could still end up with less money than I started with, if I hold the bond until maturity. Ultimately, the only scenario where I would want to buy a bond with a negative yield is because I anticipate deflation and even lower rates in the future. Is this correct, or is there another reason?  Currently, a lot of the global government bond market is trading on negative yield, and there are even some corporate bonds that are too. A children's book series about a farm that grows massive food There was a series of illustrated children's books that I was introduced to as a child in the late 1980's early 1990's.  The main character was a farmer - I can't remember the name, but I think it was Mc or Mac something. He bought his farm from a sleazy character who was trying to cheat him. The farmland was originally some kind of swampy land, but this industrious character (and his family) discovered that the land would grow plants to a massive size - radishes the size of basketballs, etc.  There were some pretty fantastic stories and adventure that the character would get into, such as one winter the weather got so cold that the wind (not the air) outside froze. They went out and cut it up and stored it in the icebox and would thaw out some of the cold breeze later in the hot summer.  The sleazy character made a constant appearance, trying to swindle this family out of the farm.  My Google-Fu seems to fail me at every turn. Do you know what this series is? Serializing anonymous delegates in C# Last two digits of $2^{1000}$ via Chinese Remainder Theorem? I bumped across the aforementioned question in my notes while studying today and I have completely forgot how to do this. I remember using CRT to solve a problem like this on one of my tests, too bad they didn't give back my solutions :(.  Since $\gcd(100,2) = 2$, we can't use the usual Euler's theorem to solve via $\pmod {100}$. So $100 = 5^2 2^2$, and applying Euler's on the 25 gives me $2^{20} \equiv 1 \pmod {25}$. However since $\gcd(2,4) = 2$, we can't do the same for $\bmod 4$. Accordingly how do I set up the other modulo congruence so I can apply CRT? How does an internet server respond to a request from a private IP? Combination with repetitions.