The rep count for "today" has many issues
Expanding an event group shows more events than labeled when there are new events
How can i show that two $R$-modules of finite rank are isomorphic if and only if they have the same rank, i.e., $R^n \cong R^m$ iff $n=m$. How is the zero flag set in terms of hardware? Create a local texmf tree in MiKTeX Use the triangle inequality to show that $|a|+|b| \leq |a+b|+|a-b|$ How would I go about proving that  $$|a|+|b| \leq |a+b|+|a-b|$$  Using the triangle inequality?  I tried squaring both sides, yielding:  $$|a|^2 +|b|^2 +2|a||b| \leq 2|a|^2+2|b|^2+2||a|^2-|b|^2|$$  Is it correct to move the terms to the other side? I tried $$2|a||b| \leq |a|^2+|b|^2+2||a|^2-|b|^2|$$ Then it is obvious that  $$0\leq |a|^2+|b|^2-2|a||b| +2||a|^2-|b|^2|$$ $$0\leq (|a|-|b|)^2 +2||a|^2-|b|^2|$$ $$0\leq ||a|-|b||^2 +2||a|^2-|b|^2|$$  But I have neither used the triangle inequality, nor it looks mathematically rigorous for my real analysis class. Any tips and tricks for solving these problems? Minecraft jar not marked as executable I want to be able to lock my translation/scale operations to two axes at a time, say xy, xz or yz. It currently takes two operations (one for each axis).  Example, say for a cylinder, I would like to reduce the radius. I currently have to scale on the x axis first, then on the y axis, or I have to manually input the scale values in the object properties panel.  This option is easily accessible in 3dsmax via the axis constraints command bar. Or I can click the intersecting area between the 3d manipulator of the axes in question and move in that plane. A groupoid is defined to be a category where every morphism is an isomorphism. So sometimes a group is said to just be a groupoid with one object.   When I try to make sense of this, I denote the single object as $G$. I view the morphisms as the analogue of "elements." The identity $1_G$ is the analogue of the usual identity $e$, we can compose any two morphisms since they are all arrows on $G$, and for any arrow $f$, we have some $f^{-1}$ such that $f\circ f^{-1}=f^{-1}\circ f=1_G$, so the idea of inverses is still there.  So I informally associate the elements of the group in the usual definition to be the arrows in the groupoid. But what does the sole object $G$ in the groupoid "correspond to" if I were to try to informally make sense of a group in the usual sense? Does it even correspond to anything? What term refers to those who adhere to scientism? How can I find and replace specific words in a text file using command line? How can a question banned user fix their questions if they're deleted? If a user is question banned  and the , how can the user fix this on their own?  Until recently, advice has been to improve their questions, but since they can't see the questions on their question screen, they can't improve them:     Feature request: Allow a question banned user to see their own deleted questions, or warn them that deleting questions could lead to a question ban. Duplicate questions in feed, and questions incorrectly marked as unanswered I see duplicate questions in the feed (Why is the book still wanted if Aida has memorized it?) and the question is marked as "unanswered" even though it has an upvoted answer.  I would expect unique questions in the feed, as well as questions with answers to not be marked as unanswered.   App Version: 1.6.3.4 Device: iPhone 6 OS Version: Version 10.2 (Build 14C92) access parent object in javascript Update Manager asking me to update kernel but apt-get upgrade does not? I often read that in case of Deep Learning models the usual practice is to apply mini batches (generally a small one, 32/64) over several training epochs. I cannot really fathom the reason behind this.  Unless I'm mistaken, the batch size is the number of training instances let seen by the model during a training iteration; and epoch is a full turn when each of the training instances have been seen by the model. If so, I cannot see the advantage of iterate over an almost insignificant subset of the training instances several times in contrast with applying a "max batch" by expose all the available training instances in each turn to the model (assuming, of course, enough the memory). What is the advantage of this approach? What's the difference between iterating over a file with foreach or while in Perl? How long does it take for chat profiles to update? Following scenario:   user registers, has 1 point user visits chat, notes he cannot post because of only 1 point and needs 20 user goes back to SO, answers a question. gets enough points to chat user goes back to chat, but his profile still shows 1 point   Now my questions:   How long does it take for the profile on chat to update? Is there a way to force updating?   Update: Logging in and out did not help. Is solving all of the exercises in a textbook a good idea? Is solving all of the exercises in a textbook a good idea? I'm particularly concerned with textbooks on mathematics. I have this obsession that I should solve all of the problems that a textbook has. It takes a lot of time and energy but usually I'm satisfied with the end result being me having a better understanding of that particular subject.   Any similar experience of this sort? How's this going to work in the long-run? If I my motherboard is SATAI, can it use SATAII hard drives? How to pass a list of columns to data.table where some are predetermined Cannot add a NOT NULL column with default value NULL in Sqlite3