Can I extend mathematical induction to real numbers?
Induction on Real Numbers
Is it possible to skip releases during an upgrade? Possible Duplicate:          Is it possible to upgrade a 10.04 lucid installation to 11.04 Natty, without upgrading to 10.10 first? What about other versions? I recently got my Blacksmithing skill to 100. Now in the skills menu I can press space to make it Legendary, which will put it back to a skill level of 15 and reset my perks.  I am wondering: What benefit is there from making a skill Legendary apart from being able to level up the skill more thus having infinite levels? Generalized Tube Lemma Trying to install Ubuntu on Dell XPS 15 (9570) I have been trying to install Ubuntu on my new laptop:     Dell XPS 15 (9570)   Windows 10 Home 64bit English   8th Generation Intel(R) Core(TM) i7-8750H Processor (9M Cache, up to 4.1 GHz, 6 cores)   16GB, 2x8GB, DDR4, 2666MHz   256GB M.2 2280 PCIe Solid State Drive   NVIDIA(R) GeForce(R) GTX 1050Ti with 4GB GDDR5     I began by trying to install Ubuntu 18.04 LTS using an 8GB USB drive. The first issue I ran into was getting frozen on the bootup screen on the fourth dot. After a couple tries, I plugged in my monitor (through HDMI) and it stopped getting stuck all of a sudden.    Next, I tried to go through the installation and when I clicked on restart now, my computer froze and I had to shut it down manually and start it back up again. At this point I got to the login screen and logged in but after entering my password it got stuck on a purple screen with my mouse pointer (which was frozen). I was able to get into a shell at this point (with ctrl+alt+f4) and attempted to run sudo apt-get install nvidia-390 but this froze when it reached building initial module for 4.15.0-22-generic and upon reboot I had to run sudo dpkg --remove -a.    I was unable to work around this so I attempted to install Ubuntu 16.04 which I could only do by adding acpi=off to the boot configuration (which by the way, I had a lot of trouble getting to since GRUB usually flashed in and then immediately disappeared and only occasionally would it stick around long enough for me to use). But when I try to boot up now, I never reach the screen with the five dots and instead immediately get stuck on a purple screen (with no mouse pointer).  I reinstalled Ubuntu 18.04 and am back to being stuck on the log-in screen.  What should I do? Changing my iTunes account details Sunlight Sensitivity looks pretty bad — Disadvantage to attack rolls and Perception checks whenever you, your target, or what you're trying to perceive are in direct sunlight. I hope I'm missing something, since no other PC race has a comparable hindrance.  Are there any ways you have used to mitigate this flaw to make players of this race not at a severe disadvantage (or, if it doesn't need mitigation, explain why it's already balanced without any action required)? How do I install pillow in Ubuntu 16.04 LTS? Do you need to disavow on [HTTPS SSL] after performing a disavow on [HTTP] I have a client which disavowed a few thousand dirty links from his site profile back in February 2015. Recently the site was switch from HTTP to HTTPS (SSL enforced).   Google recommends that you add all variations to the Google Console (Webmaster Tools).  The site has a total of 4 variations, eg:    http://www.example.com (Previously Preferred) http://example.com https://www.example.com (Now Preferred) https://example.com   Question:  Since technically this is a new property in Google Webmaster Tools, do you need to submit the same disavow file added previously back in 2015? Do I need a transit visa for a layover in the United Arab Emirates? Do I need a transit visa for a layover via airports in the UAE, such as Dubai International Airport or Abu Dhabi International Airport? If so, what are the requirements for such a visa? Can I get the transit visa on arrival? Let $f$ be a continuous function. If $f$ is uniformly continuous then it maps cauhy sequence into cauchy sequence. Is the converse true? That is if $f$ maps cauchy into cauchy gives the uniform continuity of $f$. I think it's no. Can suggest a counter example How to get from Heathrow Airport to King's Cross, London? My wife and I will be arriving in London via Heathrow Airport (LHR) and are staying at a hotel near King's Cross station. So, we were wondering what the best (which means fastest but also easiest when carrying two large pieces of luggage and two carry-ons) way to get from LHR to King's Cross?  I gather that, with only one changeover, we can take the Tube. However, in the interest of other passengers, we thought it would be best to take a taxi, or maybe a bus?  Thoughts? Calculating the area of an irregular polygon Given the length of the sides of an irregular polygon (no coordinates provided) how do you compute the area of the maximum area of the polygon?   Thanks in advance I'm  trying to create a FPS game in blender game engine. When I do KeyBoard[Spacebar] sensor and hook it up to a simple motion of z +1 or something like that, the guys pops up really fast as if he didn't have any motion between being on the ground and being in the air. Is there a way to make a more realistic, more slow jump in BGE? I can't read beta sites' chat logos! Here, you try:  If it weren't for the text shadow, it might as well be entirely invisible...  The cause is a CSS rule lurking in the transcripts for beta sites only:  #transcript-logo {   background: none repeat scroll 0 0 #273A5D; }   The problem is the #273A5D - a bluish colour not dissimilar to that used for the site name in the beta theme. Disabling that rule yields the much more manageable  I'll admit it is a little hard to read the "beta" in that shot. But if you had to choose which part was readable, wouldn't you choose the bit that tells you the name of the site?  Edit: It happens when actually in a chat room too! I ask this Question on behalf of my neighbor.   Their 12 year old son saw his parents having sex.  As there is only one room in their home we can't say its the parents' mistake... but now the question is how do they handle the situation? "To be subject to" vs. "to be subjected to" The script I use is actually returning this output:  (source /Thetra/Commun/env_ora.sh &gt;/dev/null; sh aclenv/arun)  geIlgif0t1 -DVORACLE geIlgif0t1 prg_25900: ACOMP=X geAhadlAd1 -DVORACLE geAhadlAd1 prg_25948: ACOMP=A syCcgge0t1 -DVORACLE syCcgge0t1 prg_26023: ACOMP=S2 syVcalq0t1 -DVORACLE syVcalq0t1 prg_26071: ACOMP=Y syVvali0t1 -DVORACLE syVvali0t1 prg_26119: ACOMP=Y syAedit0t1 -DVORACLE syAedit0t1 prg_26167: (1312) DBMS WARNING: Column not found in table. (-11238)   RETURN (-6)     END  END     END     IF cm_para_f2('VDEF','abQtip_0n1','unicite',syAedit0t1:$v_unicite)&lt;&gt;0      OR null_convert$(syAedit0t1:$v_unicite,'R') &lt;&gt; 'F' THEN SET syAedit0t1:$v_unicite TO 'R'     SET $v_tips_mrgl TO 'S'     SET $v_rfbt_iban, $v_rfbt_intitule, $v_orga_creancier, $v_orga_tip_adr1, $v_orga_tip_adr2,         $v_orga_tip_adr3, $v_code_docu, $v_tips_centre, $v_code_etab, $v_orga_tip_emetteur,  $v_orga_emetteur, $v_rfbt_compte, $v_orga_banque, $v_rfbt_emetteur TO     SELECT rfbt_iban, rfbt_intitule, orga_creancier, orga_tip_adr1, orga_tip_adr2, orga_tip_adr3 ACOMP=N syAvali0t1 -DVORACLE syAvali0t1 prg_26215: (2751) DBMS WARNING: Column not found in table. (-11238)  + to_string_using$(str_to_val$(substr$(clip_str$(to_string$($f_imme_no)),1,4)),'&amp;&amp;&amp;&amp;')         + to_string_using$(str_to_val$(substr$(clip_str$(to_string$($f_sepa_propriete_no)),1,5)),'&amp;&amp;&amp;&amp;&amp;')     IF syAvali0t1:$v_unicite ='R' THEN  SET $v_sepa_rum3 TO $v_sepa_rum3 + substr$(to_string_using$(syAvali0t1:$v_ordr_direct,'&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;'),7,9)     ELSE ACOMP=N syAcalc0t1 -DVORACLE syAcalc0t1 prg_26263: ACOMP=N syAcalc0t2 -DVORACLE syAcalc0t2 prg_26311: ACOMP=N syAcalc0t3 -DVORACLE syAcalc0t3 prg_26359: ACOMP=N   To check for errors I use the following command:  (source env_ora.sh &gt;/dev/null; sh aclenv/arun) | egrep '^ACOMP=$'   Output:  (1312) DBMS WARNING: Column not found in table. (-11238)   RETURN (-6)     END  END     END     IF cm_para_f2('VDEF','abQtip_0n1','unicite',syAedit0t1:$v_unicite)&lt;&gt;0      OR null_convert$(syAedit0t1:$v_unicite,'R') &lt;&gt; 'F' THEN SET syAedit0t1:$v_unicite TO 'R'     SET $v_tips_mrgl TO 'S'     SET $v_rfbt_iban, $v_rfbt_intitule, $v_orga_creancier, $v_orga_tip_adr1, $v_orga_tip_adr2,         $v_orga_tip_adr3, $v_code_docu, $v_tips_centre, $v_code_etab, $v_orga_tip_emetteur,  $v_orga_emetteur, $v_rfbt_compte, $v_orga_banque, $v_rfbt_emetteur TO     SELECT rfbt_iban, rfbt_intitule, orga_creancier, orga_tip_adr1, orga_tip_adr2, orga_tip_adr3 (2751) DBMS WARNING: Column not found in table. (-11238)  + to_string_using$(str_to_val$(substr$(clip_str$(to_string$($f_imme_no)),1,4)),'&amp;&amp;&amp;&amp;')         + to_string_using$(str_to_val$(substr$(clip_str$(to_string$($f_sepa_propriete_no)),1,5)),'&amp;&amp;&amp;&amp;&amp;')     IF syAvali0t1:$v_unicite ='R' THEN  SET $v_sepa_rum3 TO $v_sepa_rum3 + substr$(to_string_using$(syAvali0t1:$v_ordr_direct,'&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;'),7,9)     ELSE   We can see that grep is returning non matching lines.  When I redirect the stderr to stdout with this command:  (source /Thetra/Commun/env_ora.sh &gt;/dev/null; sh /Thetra/Oracle/transfert/P2016.H.1/aclenv/arun) 2&gt;&amp;1 | egrep '^ACOMP=$'   As expected, the output is void.  Why grep is returning non matching lines when stderr is not redirected ? I am using Ubuntu 16.04, with Gnome 3.18. Using extensions I have gotten rid of the dash panel and only use the Applications Menu in the upper left-hand corner of the screen. (I don't have Unity.) What I can't figure out is how do you add a new program, move software around to different categories, and create new categories?  Also, any keyboard shortcut to access the Applications Menu? My old computer broke down a few days ago, so I'm using a laptop until I can get it fixed.  As a side effect, I no longer have my usual browser cookies, so I had to log back into Stack Exchange.  While doing so, I noticed that I kept having to log in to every Stack Exchange site I visited &mdash; the usual "Welcome back [username], you've been logged in." auto-login banner seemed to be conspicuously missing.  In fact, a quick look at the "network" tab in the developer tools suggested that no requests to stackauth.com were being made at all.  Eventually, I decided to dive into .  Turns out that the code to make the global auth check and bring up the banner is simply:    gauth.checkStackAuth(StackExchange.options.stackAuthUrl);   And, what do you know, running that command from the developer console does auto-log me in.  However, the reason this code isn't being run automatically is because it's disabled in the site config (apparently for all SE sites).  For example, the page I'm typing this question on has the following config options set:  StackExchange.init( {     "locale": "en",     "stackAuthUrl": "https://stackauth.com",     "serverTime": 1408393334,     "networkMetaHostname": "meta.stackexchange.com",     "styleCode": true,     "enableUserHovercards": true,     "site": {         "name": "Meta Stack Exchange",         "description": "Q&amp;A for meta-discussion of the Stack Exchange family of Q&amp;A websites",         "isNoticesTabEnabled": true,         "recaptchaPublicKey": "6LdsB7sSAAAAAAzjgEF_Hd8vXv-C42sa_KyofaGR",         "recaptchaAudioLang": "en",         "enableNewTagCreationWarning": false,         "globalAuthDisabled": true,                // &lt;--- HERE         "isMetaSite": true,         "enableSocialMediaInSharePopup": true,         "useGoogleOAuth2": true     },     // etc.   So, apparently, global auto-login has been deliberately disabled for some reason.  Why is that, and is there any planned timeline for re-enabling it? How to make Gmail automatically label incoming emails I would like to set it up so that Gmail labels incoming mail based on which business email of mine the emails are sent to. I have two business emails that come to my Gmail account.  For instance, if someone emails me at example@firstbusiness.com, I would like the email to be automatically labeled first business. If someone emails me at my other email address (which also is forwarded to Gmail), example@secondbusiness.com, I would like that email to be automatically labeled second business.   Is there any way to do this?