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While studying the Fibonacci sequence I encountered this problem in the handout, and I can not understand how to do it.     Show that if the Fibonacci sequence has a term divisible by a natural number $m$, then there are infinitely many such terms. On the bash command-line, ↑ gives me the previous command. On the command-lines in ipython or matlab, when I type a few characters, ↑ gives me the previously entered command starting with those characters. How can I enable exactly this behaviour in bash? I am aware of more advanced ways of searching through the command-line history, but sometimes a simple way is more convenient. In Java, is there any way to use the JDK libraries to discover the private classes implemented within another class? Or do I need so use something like asm? How unusual is getting a Masters degree in a slightly different field than Bachelors? Would it be out of the ordinary to get a Bachelors in Mechanical Engineering and then go for a Masters in something like Civil or Structural Engineering?  I don't know a lot about how transitioning to a Masters program works.. Do people usually continue on in the same field, or is branching out common? How do I remove gapps from CyanogenMod I installed CyanogenMod 11 on my HTC One with CyanogenMod Installer. So I got also the google Apps (gapps) on my device. But I need a CM11 without gapps. I did then the following without success:   copy cm-11-20140308-SNAPSHOT-M4-m7.zip to /sdcard/ boot to recovery mode -> recovery -> ClockworkMod Recovery v6.0.4.6: "wipe data/factory reset" "install zip" choosing the zip-file "reboot system now"  So I got a new CM11 but with gapps still installed.  What should I do in addition to "wipe data/factory reset" to get rid of this apps? Why do heavier objects fall faster on hills but not in straight drops? All other things being equal, if a heavier object will roll at a higher speed down hill than a lighter one, because it's heavier with more mass, then how is it that dropped objects fall at the same speed regardless of their weight? Is a set without limit points necessarily closed? According to the definition on Rudin' Principles of Mathematicial Analysis, closed set is defined as:      $E$ is closed if every limit point of $E$ is a point of $E$.   Then I have a question: if a set has no limit point, is it necessarily closed? I think this idea doesn't contradict the definition of closed sets. Am I right?  And another question is #10 in Chap.2 of Rudin's:      Let $X$ be an infinite set. For $p\in X$ and $q\in X$, define    $d(p,q)=0$ when $p=q$. Otherwises,$d(p,q)=1$.    I have known that every set in the metric space is closed. To prove it, we can show that the complement of any set is open, which is quite trivial. My question is: how can we prove that every set is closed just by checking according to the definition of closed set, i.e. how can we show that every limit point of any arbitrary set $E$ in the metric space is a point of $E$?   Thanks in advanced! Is it possible to have a monoid with a proper class as the collection of elements? My question if it possible for us to have, for example, a monoid(any algebraic structure really) with a class as the collection of the elements, instead of a set.  An example would be the class of sets and set union as addition. Clearly, it is closed under the operation, is associative and it has an identity element, so it is a monoid. Is it possible to say so? Can an Indian citizen holding a valid USA visa visit Colombia without a visa? I am planning to travel to Colombia for about a week to attend an academic conference. I am an Indian passport holder currently living in USA with a F-1 visa. Do I need to obtain a visa beforehand from the Colombian consulate?  I have found   that claim that Indian citizens holding a valid USA visa are not required to apply for Colombian visa.     However, I am not sure if these sources are "official" and trustworthy.Is there a more official source? Also, does this rule apply to "tourists" only? Does anyone have any personal experience with this rule? So, Can linking verbs be used with "continuous tenses"? Is there any evidence or reason why FIFA is so against adding instant replay to soccer? I find myself seeing many unlucky or just plain wrong decisions made by refs that could be corrected with instant replay. Prove that  $ n &lt; 2^{n}  $ for all natural numbers $n$.  I tried this with induction: Inequality clearly holds when $n=1$. Supposing that when $n=k$, $k&lt;2^{k}$. Considering $k+1 &lt;2^{k}+1$, but where do I go from here?  Any other methods maybe? What can I do when getting "We are no longer accepting questions/answers from this account"? If you are reading this, you may have been affected by one of our post quality bans. If so, it is important that you  to understand what has happened and how to regain the permissions that you lost. While trying to ask a question, one could see:  We are no longer accepting questions from this account. See  to learn more.  Likewise, for answers:  We are no longer accepting answers from this account. See  to learn more.   Why am I getting this message? Are deleted posts taken into account too? Is a question/answer ban the same as a suspension? How do I avoid getting a question ban? How long do I have to wait before I can post again? What can I do to release the ban? How can I reactivate my account? Can I simply create a new account? I'll just ask somewhere else on the SE network, and they'll migrate my question to the correct site! Will a ban on one Stack Exchange site affect my standing on other sites in the network? Does this apply to meta sites too? My account is in good standing. Why am I still blocked? Shadow Incorrect at Bottom of Edge A Strict Sense Stationary (SSS) process implies it is a Wide Sense Stationary (WSS) process - proof Looking for a mathematical proof which shows that a Strict Sense Stationary (SSS) process is necessarily a Wide Sense Stationary (WSS) process. When should a verb be followed by a gerund instead of an infinitive? CDF of absolute value of difference in random variables In chrome, most of the time, when i middle click on a link (text or image), it opens a new tab and the current tab does not change. This is the expected behaviour.  However, some websites have links (i'd say 5%) that also switches the current tab to the new one. For example: on this , the name of the players in the main list have the problem.  By looking at the source, i didn't find anything anormal (the link is a standard html tag). But if i disable javascript, i have not the problem. I looked at the source, and didn't find the problematic script... Note also that if i open the tab with right click > open link in new tab, there is no problem.  I'd like to know if you find the reason of the problem and how i can fix it. I am running chrome 10.0.648.204 on windows 7 x64.  EDIT: the website above does not exhibit the behavior anymore, but I sill have the problem sometimes on other sites (which I don't remember) Understanding a derivation of bias correction for the Adam optimizer I'm reading  about the Adam optimizer and went up until the bias-correction section; in the paper they estimate the bias of the moving average of the squared gradient. These are the equations they use:    Where $v_{t}$ is the moving average of gradient squared, $g_{i}$ is gradient at the $i^{th}$ iteration and $\beta_{2}$ is a moving average parameter.  I don't understand how they make any of these transitions from the first row to the second and on to the third one. Could someone explain what rules are allowing them to do so ? The binomial sum   $$s_n=\binom{n+1}{0}+\binom{n}{1}+\binom{n-1}{2}+\cdots$$   satisfies the Fibonacci relation.   I failed to prove that $\binom{n-k+1}{k}=\binom{n-k}{k}+\binom{n-k-1}{k}$... Any hints or suggestions?