I was married before and had 3 children.  My wife and I got divorced and have since remarried other people. My new wife and I had a son together and my ex wife and her new husband  had a son. These two young boys will be only related by their older siblings. Is there a name for what they are? I've searched the web but cannot find a term
Here at the Genealogy and Family History Stack Exchange we see many questions about relationship mapping which is also known as:   relationship calculation kinship terminology etc   If you are just trying to understand how to calculate "cousins and removes" then  provides an excellent guide.  However, if you are seeking an English term for a more complicated relationship between two members of an extended family, rather than asking a question like:          site users are encouraged to first review the answers below.    Note: This Q&amp;A arises from  and is set to  to help make it canonical.
How do I go about proving this? I know one method is:  $\eqalign{    \cos (90^\circ + \theta ) &amp;\equiv \cos90^\circ \cos\theta  - \sin90^\circ \sin\theta   \cr    &amp;  \equiv (0)(\cos\theta ) - (1)(\sin \theta )  \cr    &amp;  \equiv  - \sin \theta  \cr} $  I'd appreciate others, particularly ones that will allow me to visualize this identity on the unit circle.  Thanks alot. I am trying to remember the title of a children's SF book I once read, maybe 20 to 25 odd years ago.   I don't have a great number of details (and some of what I recall may be completely wrong), but the details (such as they are):   A war between two alien groups ended, and some technology that should have been destroyed was instead imprinted into a human baby. A few years later, both groups find this out and attempt to retrieve it. The main characters are the child, and an alien that I believe was called "Yacob" (or similar) who was sent to protect the child/retrieve the technology, and the antagonists were the other group of aliens that had previously lost the war and were trying to get the technology to start it up again (again, I don't remember the exact details, but I think it was a fairly simple black &amp; white/good vs. bad scenario, being a children's book and all). There was a scene in which Yacob/the alien gives the child blue food, who complains that it's blue, and the alien states "close your eyes and it's just food". The alien had a space shuttle/some other piece of tech disguised as a van. I vaguely recall a scene in which it is under attack and it flies or something. My current understanding:  $\vdash$ is "syntactic consequence", e.g. if we have $a \vdash b$ it means if we've written down $a$ as something we know, we can immediately write down $b$ as something we know. This is saying nothing about whether any of these pieces are true, false, something else, etc, it's just saying that we can say something about $b$ by virtue of being able to say something about $a$.  $\vDash$ is "semantic consequence", e.g. if we have $a \vDash b$, then it (usually) means if $a$ is always true in every interpretation (i.e. no matter how we mess with any of the underlying variables driving $a$'s valuation), then $b$ is true as well. However I don't know if this is necessarily just a "true"-only thing. It seems conceivable that we could make one for falsehoods too, i.e. if $a \vDash b$ might mean if $a$ is always false then $b$ is always false, of if $a$ is always "dog" then $b$ is always "dog", etc. But I am unsure of this one.  $\to$ is material implication, which exists solely within the logic system (as opposed to the previous two metalogical relations) and has a specific semantic meaning / definition in terms of a truth table in something like prepositional logic ($a \to b$ is always true unless $a$ is true and $b$ is false). It's defined this way simply because it is a helpful / useful model to describe things like "whenever $a$ is true, $b$ is true".  Do I have the right idea so far? Gray iTunes album tracks I noticed that a few tracks from an album appear gray.    The tracks are downloaded, I can play them if I double click them explicitly, but they don't play as part of the album. If I click the album's "play" button, they're skipped (1 gets played, then 3, then 4, etc.)  Why is this happening and how can I prevent it?    I saw a similar question, , but that's not what I'm experiencing — for me, the songs do get downloaded and everything appears to be OK, they just get skipped when playing the album. How do I check the status of the CMOS battery? Can I visit the UK with an EU permanent residence card? how to fix the width of the columns in the latex table? I have a table with long heading names. I want to fix the the width of the columns. When I do so the text flows out if the column. Any suggestion about fixing it.  Here is the example   \begin{table*}[ht] \begin{tabular}{|l|r|r|r|r|r|} \hline Image &amp; Score  &amp; here is a lot of text &amp; agian a lot &amp;a lot and a lot&amp; and the same here\\ \hline a \(left\) &amp; 1 &amp; 1 &amp; 1 &amp; 1 &amp; 1  \\ \hline b \(right\)&amp;  1 &amp;1 &amp; 1 &amp; 1 &amp; 1  \\  \end{tabular}  \end{table*} I'm reading . Then I'm not able to figure out the difference between hard voting and soft voting in context to ensemble based methods.  I quote descriptions of them from the book. The first two images from the top are description for hard voting, and last one is for soft voting.        In my view hard voting is majority decision, but I don't understand soft voting and the reason why soft voting is better than hard voting. Would anyone teach me these? Is a variable/arbitrary element a precisely defined mathematical object? Ethernet device not managed I am using Ubuntu 16.10 and recently I have not been able to connect to internet using Ethernet. The network manager shows device not managed. The WiFi network is working fine.      I've tried the solution from this questionn  with no use.  My /etc/network/interfaces file:  # interfaces(5) file used by ifup(8) and ifdown(8) auto lo iface lo inet loopback   My /etc/NetworkManager/NetworkManager.conf file:  [main] plugins=ifupdown,keyfile,ofono dns=dnsmasq  [ifupdown] managed=true   Output of nmcli d:  DEVICE  TYPE      STATE      CONNECTION  wlp2s0  wifi      connected  eduroam     enp8s0  ethernet  unmanaged  --          lo      loopback  unmanaged  -- What can cause a question to be "bumped" to the first page in the Active tab of a Stack Exchange site? (Changing the "Last Active" date.)  . I tried to log into Minecraft today to find that my password isn't working. I tried to change it, but I can't login to my email because I forgot the answer to my security question. I tried changing the email to a different one, but that didn't work for some reason (it kept saying "invalid email"). I don't have my transation ID because I forgot which credit card I used.  Does this mean that I have to buy a new Minecraft account? Proving that ${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k} $ How can I prove that $${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k} $$  I tried the following:  We use the :  $$y^{\underline k}=\underbrace{y(y-1)(y-2)\ldots(y-k+1)}_{k\text{ factors}},$$ so that $\binom{y}k=\frac{y^{\underline k}}{k!} .$   Then  $${x +y+n- 1 \choose n} = \frac{(x +y+n- 1)!}{n! ((x +y+n- 1) - n)!} =  \frac{1}{n!}. (x +y+n \color{#f00}{-1})^{\underline n} $$  And  $$ {x+n-k-1 \choose n-k}{y+k-1 \choose k}$$ $$\frac{1}{(n-k)!}.(x+n-k-1)^{\underline{n-k}}.\frac{1}{k!}.(y+k-1)^{\underline{k}}$$ $$\frac{1}{k!.(n-k)!}.(x+n-k-1)^{\underline{n-k}}.(y+k-1)^{\underline{k}}$$ $$\sum_{k=0}^n{n \choose k}(x+n-k-1)^{\underline{n-k}}.(y+k-1)^{\underline{k}}$$  According to the Binomial-coefficients:  $$ ((x+n-k-1) + (y+k-1))^{\underline{n}}$$ $$ (x+y+n\color{#f00}{- 2})^{\underline{n}}$$  What is wrong ? und How can I continue?  :/ How Can I Butcher Animals en Masse? So, my friend just implemented a bunch of new mods into his SMP server, which meant a host of new commands to play with.  I thought I'd give the /mobspawn command a few goes, and see what I could achieve.  So I headed off to the server's jail (I forget why this particular location compelled me), and gave it a few spins.    I seem to have made a bit of an error in judgement.     What can I do to get rid of this mess?  Is there a command or some other technique I can use to clear out any mobs in my immediate vicinity? What does the dot mean Google Sheets QUERY won't display cell text if other cells have numbers I'm not sure what is happening in my Google Sheet query and could really use some help. I have  that demonstrates and explains the issue.   Basically, I'm using a query to pull data from a Google Spreadsheet that is populated by a Google Form. If the form submits only numbers (100), there is no problem. However, if someone submits a string ($100 or 100 dollars), the query will not display the string. It will only display form submissions that are 100% numbers.   Also, if the 1st submission is a string (not 100% numbers) the query will work.   Here is my query  =query(data!B2:CL,"select B, C, D, E, F, G, H, I, J, CI, BZ, CA, BA  where J = 'Industry Certification'",false)   Any ideas on why this is happening?  Also, I'm aware that I can limit the form to numbers only. I'm trying to avoid that and learn 'why' this is happening. QGIS Processing - Additional Creation Parameter for GdalWarp I am having a hard time getting the "Additional Creation Parameters" to work when using GdalWarp through the processing toolbox.  I am trying to set the nodata value to 0 for the output raster.  processing.runalg("gdalogr:warpreproject","InRaster.tif","EPSG:32736","EPSG:32736",10,0,"-dstnodata 0","OutRaster.tif")   Has anyone used this functionality and managed to get it to work? I have B1/B2 Visa. Can I travel for Business trip to US with this Visa? siunitx tabular numbers with separated uncertainty I would like to format the space reserved for a number shown in a table with separated uncertainty. It seems that when I use the table-format option the brackets around the mantissa disappear. This is illustrated in the example below:  \documentclass{article}     \usepackage{siunitx}  \begin{document}     \begin{table}   \begin{tabular}{                   S[separate-uncertainty = true]                   S[table-format=1.1(1)e1,                   separate-uncertainty = true]                   }     {Header} &amp; {Header}\\     1.0(2)e2 &amp; 1.0(2)e2\\   \end{tabular} \end{table}     \end{document}     I have also tried to use the bracket-numbers and multi-part-units = brackets without solving this issue. Is there any workaround to center the number and keep the brackets like in the first column of the example? Using Unicode Zero Width Spaces allows all space comments