I was wondering if anyone could confirm if this sentence is correct?  It somehow doesn't sound or feel correct but I saw it written today. Can anyone give me any insight if it is right or wrong?  'But for my father, I wouldn't have achieved anything.'
Does 'but for' mean:  'If we had X (but we didn't), Y would have been the consequence'?  Or can it also mean; because we had X, as a result Y happened?   Some different examples of but for:  (Case 1)     But for a cup coffee, it was to be a productive day of writing.   Unfortunately, I'd run out, and spent the day craving.    (Case 2)     But for the glass of wine I had dinner, the house work didn't get   done.   (Case 3)     But for the glass of wine I had for dinner, I would have got the   house work done   What is the correct usage of "but for"?
Is there a specific purpose in terms of efficiency or functionality why the k-means algorithm does not use for example cosine (dis)similarity as a distance metric, but can only use the Euclidean norm? In general, will K-means method comply and be correct when other distances than Euclidean are considered or used?  [Addition by @ttnphns. The question is two-fold. "(Non)Euclidean distance" may concern distance between two data points or distance between a data point and a cluster centre. Both ways have been attempted to address in the answers so far.] Determine pid of terminated process Parenthesis in expr arithmetic: 3 * (2 + 1) how to reduce DC voltage using resistors? How would one go about using a 12 V DC power source to power something which needs 4.5 V DC using resistors? Is there a way to determine how much adding a resistor would drop the voltage? I have recently started reading and watching Naruto. I was wondering in what aspect does the clones made by different techniques differ? They all have the same potential and capabilities. My online friend is asking for money in order to visit my home country. Is this a legit request or a scam? On Travel.SE we often see questions about a person (usually a love interest) asking for money to pay for airfare, visas, permits and other expenses. For example        What general advice can be given in such situations to the person asking the question? Is it all a scam or can there be legitimate situations in which an online friend could be asking for money? 3 questions about Algebraic Geometry and Zariski topology I've read this exercise on my book, but I don't know how to prove it... Can someone help me?  Let X $\subseteq \mathbb{A}^n$ be an algebraic set, and $f, g:X\rightarrow k$ two regular functions.  a) If we see $f$ as an application $X \rightarrow \mathbb{A}^1(k)$, prove that $f$ is continuous in the Zariski topology.  b) If $X$ is irreducible and an open $U \subseteq X$ exists such that $f_{|U} = g_{|U}$, prove that $f=g$.  c) Give an example of $X, f$ and $g$ such that $f \neq g$ but $f_{|U} = g_{|U}$ in an open $U \subseteq X$.  Thank you!  For b) I have been able to prove that:  Let E be the subset where $f = g$ so E is closed (Why? I know that $E = (f,g)^{-1}(\Delta_{k})$ but... why is $(\Delta_{k})$ closed?). So $U \subseteq E \Rightarrow \bar{U} \subseteq \bar{E}=E$ (beacuse E is closed) $\Rightarrow X \subseteq E$, because $\bar{U}=X \Rightarrow E = X$ and $f=g$ in X. Compilation problem with siunitx (returning error regarding ifnum) I'm trying to get siunitx working. For some reason I keep getting this error:  ! Missing = inserted for \ifnum. &lt;to be read again&gt;                     - l.3 \begin           {document}^^M   I have tried a minimal document to make sure it is not some kind of compatibility issue. And I get that same error in the most minimal document possible.  I'm using pdfLaTeX to compile, and have tried both from TeXWorks and from bash. I'm using TeXLive, if that matters. I have also tried reinstalling siunitx, l3packages, and l3kernel. There was an issue with l3kernel before this, due to an apparently old version. But all three packages are now up to date. I've also reinstalled expl3 while trying to debug the original issue.  My minimal document is:  \documentclass{article} \usepackage{siunitx} \begin{document} \end{document}   The output I get is:  This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015/Debian) (preloaded format=pdflatex) restricted \write18 enabled. entering extended mode (./untitled-2.tex LaTeX2e &lt;2016/02/01&gt; Babel &lt;3.9q&gt; and hyphenation patterns for 81 language(s) loaded. (/usr/share/texlive/texmf-dist/tex/latex/base/article.cls Document Class: article 2014/09/29 v1.4h Standard LaTeX document class (/usr/share/texlive/texmf-dist/tex/latex/base/size10.clo)) (/home/&lt;name&gt;/texmf/tex/latex/siunitx/siunitx.sty (/home/&lt;name&gt;/texmf/tex/latex/l3kernel/expl3.sty (/home/&lt;name&gt;/texmf/tex/latex/l3kernel/expl3-code.tex) (/home/&lt;name&gt;/texmf/tex/latex/l3kernel/l3pdfmode.def)) (/home/&lt;name&gt;/texmf/tex/latex/l3packages/xparse/xparse.sty) (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty)) (/usr/share/texlive/texmf-dist/tex/latex/tools/array.sty) (/home/&lt;name&gt;/texmf/tex/latex/l3packages/l3keys2e/l3keys2e.sty) (/usr/share/texlive/texmf-dist/tex/latex/beamer/translator/translator.sty (/usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty) (/usr/share/texlive/texmf-dist/tex/latex/beamer/translator/translator-language- mappings.tex))) ! Missing = inserted for \ifnum. &lt;to be read again&gt;                    - l.3 \begin          {document}^^M ?   Does anyone have any idea what might be going wrong here? How to determine if the specific time is between given time range in javascript How do I remove login credentials (emails or OpenIDs) from my account?     For more information, see "" in the . Has anyone successfully embedded their  on a WordPress.com-hosted blog?  The free hosted version of  (not )  from all posts before publishing. So they to strip out just about anything I can add to embed my Stack Overflow flair.  Note: I'll be switching to a paid, hosted site in the future (fixing the problem), but I'm looking for a quick, short-term solution. Seeking documentation for {z}/{x}/{y} syntax in tilesource urls? Speaking of tilesource urls such as   http://{s}.tile.stamen.com/watercolor/{z}/{x}/{y}.png  is there any technical documentation or canonical reference for the curly braces syntax?  I'd specifically like to know what other things can be used in curly braces, and in which places, and how they work. How about a "Irritable" badge for someone who downvotes often? EDIT : How about a forced comment   dialog...which forces the user's to   comment when they downvote otherwise   they can't....right now it just shows   a popup to suggest posting a   comment...maybe this is little too   strict...but i just find it annoying   when ppl downvote and leave no   comments....   How about having a badge "Irritable" for a user who downvotes over 20 times in a month and then have maybe further "Furious" for over 50 downvotes in a month....just a fun suggestion...since i see people downvote like crazy at times...there should also be a way to downvote a comment i think in addition... Product of manifolds & orientability I'm studying orientability of manifolds currently and I'm having trouble to prove the following: $M\times N$ is orientable iff $M$ and $N$ are orientable.   I am able to prove that the product is orientable if components are orientable (chart is $\{(U_\alpha\times V_{\beta},\phi_\alpha\times \psi_\beta):(\alpha,\beta)\in A\times B \}$, and $\det J=\det J_1 \det J_2&gt;0$ by Cauchy-Binet's theorem), but I don't know how to prove the other direction.   So why this holds: if $M\times N$ is orientable, then $M$ and $N$ are orientable?  Thanks in advance. Direction of friction when a car turns When a ball moves to the right, friction acts to oppose the motion, in other words, to the left. However, when a car travels around a bend, the friction acts in the perpendicular direction to the car's velocity and provides the centripetal force. I just cannot understand why friction would act in that direction. Using "utilize" instead of "use"? Clip vector on Geoprocesing QGIS 2.18.13, global name 'features' is not defined I want to clip a vector polygon with a boundary vector polygon but the process is failing. I am getting the error, "global name 'features' is not defined See log for more details". I don't know what is causing this error. Given the sentence:     Most people who live and work near Washington, DC, would have trouble      imagining dinosaurs walking around the area.   Grammatically, what would ‘imaging’ be called in this case? Present participle or gerund or something?  I mean, if it is a present participle, ‘imagining~’ might be a description of the subject. And if it is a gerund, ‘imagining~’ might be an object of the verb phrase of ‘have trouble’. How do they explain this ‘imagining’ after ‘have trouble’? How prove :         $$ {31}^{11}&lt;{17}^{14} $$       help please! reason for exec in wrapper scripts