Let $A_{n}:=\{f \in  C([0,1]): \exists x \in [0,1], \forall y \in [0,1] \operatorname{so that} |f(x)-f(y)|\leq n |x-y|\}$  I have already shown that $A_{n}$ is closed w.r.t $(C([0,1]), \vert \vert \cdot \vert \vert_{\infty})$ but now I want to show that $A_{n}$ is nowhere dense, and I am given the hint of considering the linear function $s:[0,1] \to [0,C]$ with slope $\pm(n + D)$ where $D$ and $C$ are some constants $&gt; 0$.   $(\overline{A_{n}})^{c}=(A_{n})^{c}:=\{f \in C([0,1]): \forall x \in [0,1], \exists y\in[0,1] \operatorname{so that} |f(x)-f(y)|&gt; n|x-y|\}$  Let $g \in C([0,1])$ and $ \epsilon &gt; 0$: since $g$ is continuous for all $x \in [0,1]$ then there exists $\delta_{x} &gt; 0$ so that for all $|x-y|&lt; \delta_{x}\Rightarrow |g(x)-g(y)|&lt;\epsilon$  $\vert \vert g - f \vert \vert_{\infty}=\sup_{x \in [0,1]}|g(x)-f(x)|$  I am unsure on how to use the linear function $s$. Any ideas?
Let $E_n$ be $$E_n:=\{f\in C[0,1]\mid \text{exist } x_f\in[0,1] \text{ such that } |f(x)-f(x_f)|\leq n|x-x_f|,\, \forall x\in[0,1]\}.$$  How show that $E_n$ is nowhere dense, that is, $\mathrm{int}\  \overline{E_n} = \emptyset$?  Can someone help me?
How can we prove charge invariance under Lorentz Transformation? Direct Proof that $1 + 3 + 5 + \cdots+ (2n - 1) = n\cdot n$ Prove that for all integers $n$, $n \geq 1$,   $$1 + 3 + 5 + \cdots + (2n - 1) = n\cdot n$$   How would I go about proving this? For a login application, how would i go about checking the sha1 value of a password? When thinking about travelling, I often have to think about a place to visit, and then look up visa rules for that particular country. This can be a fairly painful process because official government sites can often be hard to find, and advice on (say) guidebooks or Wikitravel tends to be generic.  Is there any resource where I can enter my nationality/residency, and then look up a list of visa rules for various countries? Looking at the questions and answer to these two questions.  &amp;  and neither mentions the longevity of magic. I recall several instances of magic failing to last; the money that was spread at the  and the broken  on.  If I recall correctly when Voldemort died, the curses on several people were lifted.  I don't recall if any other spells fell apart with his death.  Is there any canon evidence on the the length of time a spell will live? Form within a block I'm using drupal_get_form('event_signup_form') to embed my custom form inside a block. The form is being rendered as intended, but submitting the form triggers nothing.  The form function itself is called event_signup_form($form, &amp;$form_state) and the submit function is called event_signup_form_submit($form, &amp;$form_state) but it's not being called.  I am using  to show the form:  function event_block_view($delta = '') { $blocks = array(); if ($delta ...) { $blocks['content'] = drupal_render(drupal_get_form('event_signup_form')); } }   I managed to get this working - here is how (stub):  function hook_block_view($delta = '') { $blocks['content'] = drupal_render(drupal_get_form('event_signup_form')); }  function event_signup_form() { // Register form submit handler, same goes for validation handler $form['#submit'][] = 'event_signup_form_submit';  return $form; }  function event_signup_form_submit($form, &amp;$form_state) { // This is now triggered } MySQL remove duplicates from big database quick I'm going through MSIL and noticing there are a lot of  instructions in the MSIL.  The MSDN article says they take no action and are used to fill space if the opcode is patched. They're used a lot more in debug builds than release builds.  I know that these kinds of statements are used in assembly languages to align later instructions, but why are MSIL nops needed in MSIL?  (Editor's note: the accepted answer is about machine-code NOPs, not MSIL/CIL NOPs which the question originally asked about.) After Upgrade to Ubuntu 20.04: "Oh no! Something went wrong" Centering sections "EOL while scanning single-quoted string"? (backslash in string) import os xp1 = "\Documents and Settings\" xp2 = os.getenv("USERNAME") print xp1+xp2   Gives me error   File "1.py", line 2  xp1 = "\Documents and Settings\"                                ^ SyntaxError: EOL while scannning single-quoted string   Can you help me please, do you see the problem? How can I filter items with a certain enchantement? I am trying to build a custom Adventure Island. At this moment I am trying to limit the allowed items on this island. I'm trying to do this by filtering on a certain enchantment which is not item-specific.  For example.   When you want to filter an wooden sword with a custom name, you use this command:  /testfor @p[r=5] {Inventory:[{tag:{display:{Name:"Custom Sword"}}}]} &lt;   When you want to filter a wooden sword with a custom name and specific enchantement, you can use:  /testfor @p[r=5] {Inventory:[{tag:{display:{Name:"Custom Sword"},ench:[{id:16,lvl:1}]}}]} &lt;   But how can I filter on items with a specific enchantment on ANY item? I tried:  /testfor @p[r=5] {Inventory:[{tag:{ench:[{id:16,lvl:1}]}}]} &lt;   But this ain't work. Does anyone know how to solve this issue? Paucity of words for relationships Please refer the following questions asked elsewhere on this site:       I am a native Hindi speaker; Hindi has a plethora of terms referring to relationships. To take a trivial example, the term uncle may refer to father's elder brother, father's younger brother, mother's brothers, father's sister's husband, mother's sister's husband, all of which have specific addresses in Hindi.  I discussed the same with one of my teachers. She had the opinion that the development of language mirrors the cultural moorings of the society that uses the language. Now, since all of the above relationships have distinct status and reverence in the Hindi speaking society, that calls for different addresses. That may well not be the case in English speaking societies.  Is that correct? What other linguistic reasons may account for such a dearth of vocabulary in English in this area? When & How often do 4e Monster powers recharge? How do I calculate standard errors for sums of OLS coefficients? Find the value of $P(1)$ Is there a theorem that says that QFT reduces to QM in a suitable limit? Of course, it should be, as QFT is relativisitc quantum mechanics. But, is there a more manifest one? such as Ehrenfest's theorem which dictates the transition from QM to Classical Mechanics.  I am curious as the basic object in QM is wave function whereas the basic object in QFT is quantized operator, which looks very different, and wondering how the comparison works.  (Of course, I am aware that QFT can calculate corrections for Coulomb potential energy, which may seem to be a transition from QFT to QM, but I want one more manifest than that.) "physical block size is 2048 bytes, but Linux says it is 512" when formatting USB - How to create a bootable USB without this error How to get things off your head in Minecraft Mo' Creatures mod I installed the Mo'Creatures mod into Minecraft, then made a fish bowl. After catching a fish I went to put it on top of a bookshelf in my room, but instead of placing it, the bowl just dropped at my feet. When I tried to pick it up my character put it on his head. Now I'm stuck with a fish bowl on my head and I can't find any mention anywhere of how to get it off. There are a number of other animals from the mod that you can put on your head for some effect, but no mention of how to remove them pretty much anywhere. Scorched3d worked then stopped. Unistalled and reinstalled did not help. Running Ubuntu 16.04.04LTS. I think it was after installing new release.  I think the problem is the Ubuntu 16.04.4LTS. The newer version has no Scorched3d in the Ubuntu Software Center. I have 3 systems. After updating to new version. Scorched3D will not install and work after updating.  ron@RonsComputer:~$ sudo objdump -p $(type -p scorched3d) | grep NEEDED  NEEDED libwx_gtk2u_adv-3.0.so.0  NEEDED libwx_gtk2u_core-3.0.so.0 NEEDED libwx_baseu-3.0.so.0 NEEDED libfreetype.so.6 NEEDED libz.so.1 NEEDED libSDL-1.2.so.0 NEEDED libSDL_net-1.2.so.0 NEEDED libexpat.so.1  NEEDED libstdc++.so.6 NEEDED libm.so.6 NEEDED libgcc_s.so.1 NEEDED libpthread.so.0 NEEDED libc.so.6   ron@ron-desktop ~ $ objdump -p $(type -p scorched3d) | grep NEEDED | awk '{print $2}' | xargs -n 1 dpkg -S  libwxgtk3.0-0v5:amd64: /usr/lib/x86_64-linux-gnu/libwx_gtk2u_adv-3.0.so.0.2.0 libwxgtk3.0-0v5:amd64: /usr/lib/x86_64-linux-gnu/libwx_gtk2u_adv-3.0.so.0 libwxgtk3.0-0v5:amd64: /usr/lib/x86_64-linux-gnu/libwx_gtk2u_core-3.0.so.0.2.0 libwxgtk3.0-0v5:amd64: /usr/lib/x86_64-linux-gnu/libwx_gtk2u_core-3.0.so.0 libwxbase3.0-0v5:amd64: /usr/lib/x86_64-linux-gnu/libwx_baseu-3.0.so.0.2.0 libwxbase3.0-0v5:amd64: /usr/lib/x86_64-linux-gnu/libwx_baseu-3.0.so.0 libfreetype6:amd64: /usr/lib/x86_64-linux-gnu/libfreetype.so.6.12.1 libfreetype6:i386: /usr/lib/i386-linux-gnu/libfreetype.so.6 libfreetype6:amd64: /usr/lib/x86_64-linux-gnu/libfreetype.so.6 libfreetype6:i386: /usr/lib/i386-linux-gnu/libfreetype.so.6.12.1 zlib1g:i386: /lib/i386-linux-gnu/libz.so.1.2.8 zlib1g:amd64: /lib/x86_64-linux-gnu/libz.so.1 zlib1g:i386: /lib/i386-linux-gnu/libz.so.1 zlib1g:amd64: /lib/x86_64-linux-gnu/libz.so.1.2.8 libsdl1.2debian:amd64: /usr/lib/x86_64-linux-gnu/libSDL-1.2.so.0.11.4 libsdl1.2debian:i386: /usr/lib/i386-linux-gnu/libSDL-1.2.so.0 libsdl1.2debian:i386: /usr/lib/i386-linux-gnu/libSDL-1.2.so.0.11.4 libsdl1.2debian:amd64: /usr/lib/x86_64-linux-gnu/libSDL-1.2.so.0 libsdl-net1.2:amd64: /usr/lib/x86_64-linux-gnu/libSDL_net-1.2.so.0 libsdl-net1.2:i386: /usr/lib/i386-linux-gnu/libSDL_net-1.2.so.0 libsdl-net1.2:amd64: /usr/lib/x86_64-linux-gnu/libSDL_net-1.2.so.0.8.0 libsdl-net1.2:i386: /usr/lib/i386-linux-gnu/libSDL_net-1.2.so.0.8.0 libexpat1:i386: /lib/i386-linux-gnu/libexpat.so.1.6.0 libexpat1:amd64: /lib/x86_64-linux-gnu/libexpat.so.1 libexpat1:amd64: /lib/x86_64-linux-gnu/libexpat.so.1.6.0 libexpat1:i386: /lib/i386-linux-gnu/libexpat.so.1 libstdc++6:amd64: /usr/share/gdb/auto-load/usr/lib/x86_64-linux-gnu/libstdc++.so.6.0.21-gdb.py libstdc++6:i386: /usr/lib/i386-linux-gnu/libstdc++.so.6 libstdc++6:amd64: /usr/lib/x86_64-linux-gnu/libstdc++.so.6 libstdc++6:amd64: /usr/lib/x86_64-linux-gnu/libstdc++.so.6.0.21 libstdc++6:i386: /usr/lib/i386-linux-gnu/libstdc++.so.6.0.21 libstdc++6:i386: /usr/share/gdb/auto-load/usr/lib/i386-linux-gnu/libstdc++.so.6.0.21-gdb.py libc6:amd64: /lib/x86_64-linux-gnu/libm.so.6 libc6:i386: /lib/i386-linux-gnu/libm.so.6 libgcc1:amd64: /lib/x86_64-linux-gnu/libgcc_s.so.1 libgcc1:i386: /lib/i386-linux-gnu/libgcc_s.so.1 libc6:i386: /lib/i386-linux-gnu/libpthread.so.0 libc6:amd64: /lib/x86_64-linux-gnu/libpthread.so.0 libc6:i386: /lib/i386-linux-gnu/libc.so.6 libc6:amd64: /lib/x86_64-linux-gnu/libc.so.6 ron@ron-desktop ~ $