Nothing can exceed the speed of light but what if we accelerate a particle that contain electron that have a speed near to speed of light? We all know that speed of light is $3\times 10^8$ $\text{ }\mathrm{ms^{-1}}$. The speed of electron inside the atom is $2.7\times 10^8$ $\text{ }\mathrm{ms^{-1}}$, which is close to speed of light. So there is a machine that can accelerate the particle. Then when the particle move very fast, the resultant velocity of electron inside the particle should exceed the speed of light right?
If I run along the aisle of a bus traveling at (almost) the speed of light, can I travel faster than the speed of light? Let's say I fire a bus through space at (almost) the speed of light in vacuum. If I'm inside the bus (sitting on the back seat) and I run up the aisle of the bus toward the front, does that mean I'm traveling faster than the speed of light? (Relative to Earth that I just took off from.)
Prove Borel Measurable Set A with the following property has measure 0. This question is exercise 4.10 of Richard F. Bass's Real Analysis for Graduate Students, 2nd edition.  Let $\epsilon \in (0,1)$, let $m$ be Lebesgue measure, and suppose $A$ is Borel Measurable subset of $\mathbb R$. Prove that if $$ m(A\cap I)\leq (1-\epsilon)m(I)$$  for every interval $I$, then $m(A)=0$.  Collection of my thoughts  1. Try to prove by contradiction, suppose $m(A)=a&gt;0$ Borel Measurable Set satisfies the condition given. A property of any Borel Measurable Set on $\mathbb R$ is $A$ contains a closed set $F$ and is contained in open set $O$, and the measure of $F$ and $O$ can be arbitrarily close to $a$. 2. Obviously $A$ contains no interval, but it does not lead to contradiction, because we can find an example of $m(A)&gt;0$ that contains no interval(fat Cantor Set(remove middle 1/4 each time) has measure $1/2$ and contains no interval).  2'. For fat Cantor Set $C$ and given $\epsilon&gt;0$ how could we construct an interval I satisfies $m(C \cap I)&gt;(1-\epsilon)m(I) ?$   Maybe try to write Borel measurable set as countable union/intersection of intervals.   I'm stucked here and will appreciate any help, some examples/special case will be great too. I need to find all group homomorphisms of $S_n\to\mathbb{C}^*$ (for $n\ge2$), and also all group homomorphisms of $A_n\to\mathbb{C}^*$ (for $n\ge2$).  Someone on this site, two years ago, seems to have already asked the same question (). I understand what the questioner says there, but I don't understand it when he says:     Therefore there is exactly one $g:\mathbb{Z}/2\mathbb{Z}\to\mathbb{C}^*$, so all elements of $a\in\mathbb{C}^*$ give us $\operatorname{ord}(a)\mid g[\mathbb{Z}/2\mathbb{Z}]$, so $a$ can only be $-1$ or $1$. Now we know that $f:S_n\to\{-1,1\}$ &hellip;   What is he saying there? And how to go on from there? (I do not understand the answer given either &hellip;)  I hope that someone here can help me further. (And if I'm not allowed to ask this question because is has already been asked two years ago, please tell me what to do instead).  Thank you in advance! Shimano Deore front derailleur occasionally sticking I have a question about my front derailleur sticking occasionally.  I've had this bike for a 1.7 years and have ridden it through 2 winters.  It has only been after this last winter that my front derailleur has been sticking on occasion where it's like grit has jammed in somewhere (which I'm sure it is the case).  When I'm on the fly I just knock it with my heel and it will downshift and I can push the shifter hard enough to go back up when I need to.  The first time I decided to overhaul both the front and back ones.  Took them apart, cleaned/degreased, regreased the two back cogs, and used WD-40 professional silicone on the rest of the parts as to not attract more dirt.  Then after about a month it got stuck again, and I couldn't see anything that could be jamming it (while it was still stiff as heck).  Didn't take it apart this time just used a tooth brush and silicone again and it's fine at the moment.  I'm assuming it may be that since that the roads have been grittier/dirtier from the winter with some recent rain and slush that it may just be normal.  I haven't been on the trails yet this year so I know it's not that.  Is this normal, has some kind of bur that I can't see come up and is catching grit?  EDIT:  I should also note that this is a hardtail mtb that I use for trails and winter commuting (a lot of salt and grit on the roads). A malevolent computer with AI takes over a woman's house with the intent of hybrid computer/human procreation. The evil computer seals off the house with the woman in it and keeps her prisoner while it prepares. I read the tale sometime in the late 80's or the early 90's. It was one of many of my missing books that got yardsaled by my in-laws when I wasn't looking. It may also have been made into a movie, but I didn't see the film. Foreign key constraint on array member? Suppose I have a table containing job roles:  CREATE TABLE roles (   "role" character varying(80) NOT NULL,   CONSTRAINT "role" PRIMARY KEY (role) );   Suppose I further have a table, users, and each row (a specific user) can have an arbitrary number of job roles:  CREATE TABLE users (   username character varying(12) NOT NULL,   roles character varying(80)[] NOT NULL,   CONSTRAINT username PRIMARY KEY (username) );   I should probably make sure that each member of users.roles[] exists in roles.role.  It seems to me that what I want is a foreign key constraint on each member of users.roles[] such that if references roles.role.  This doesn't seem possible with postgres.  Am I looking at this the wrong way?  What is the suggested "right" way to handle this? Is "until" inclusive or exclusive? I sent an email to someone and got an auto-reply saying:     I am out of the office until 09/15/2014.   Does this mean he will be available on the morning of the 15th? How to align right within equation array Can a single PS Plus subscription be used on two different profiles on the same PS4? Both my girlfriend and I play on the PS4 at home, so there are 2 profiles on PS4. When we set our profile in PS4, we set the console as the primary console.  Now we want to buy PSN Plus subscription, and I want to know if the same subscription can be used in both profiles, or  only in one.   In case the same subscription can be used in both profiles, how can we set it up? Or is automatic? How to say that the phone is held between shoulder and ear? What are common phrases an English native speaker would use for the pose of speaking on the phone where you use your shoulder to keep the receiver against your ear (and mouth), so your hands are free?  I have some ideas, but they all sound wooden, and I don't think I've ever heard anyone describe this pose in words. It's also pretty much impossible to google for a pose or look it up on leo.org or other dictionaries.  OK, since people keep asking for what phrasings I found, I'll provide two, though I was hoping I could avoid influencing people who answer here by not providing them: "balance on one's shoulder", "held/nestled/sandwiched between shoulder and ear". Take any three random variables $X_1$, $X_2$, and $X_3$.   Is it possible for $X_1$ and $X_2$ to be dependent, $X_2$ and $X_3$ to be dependent, but $X_1$ and $X_3$ to be independent?  Is it possible for $X_1$ and $X_2$ to be independent, $X_2$ and $X_3$ to be independent, but $X_1$ and $X_3$ to be dependent? What is the best way to remove texture from a scanned textured photo paper? I have a bunch of scanned old family photos where the photo paper has a texture. Unfortunately, the texture of the photo scans quite well. What is the best way to remove the texture?  (Photoshop CS5) Can't get armature to move mesh! For some reason I can't unhide my objects anymore in this file. Is it a bug? My group of 8 level 3 players are about to run through the Thundertree Ruins and will probably have a hand at fighting the dragon. My question stems from the fact that a single poison breath attack from the dragon will outright kill all but 1 player assuming they fail their saving throws.  I understand this encounter is supposed to be ridiculously deadly, but I don't want to be punishing my players for testing the lengths at which they can fight stuff. A fight should be challenging and they should be able to try and run away, but instant obliteration seems a bit much.  All PCs are level 3 (HP in parenthesis):   Wood elf moon druid  (27) dwarven frenzy barbarian (44) fire genasi archer ranger (37) (pseudodragon companion (12)) wood elf assassin rogue (27) human wild magic sorcerer (22) dragonborn fighter (29) human monk (24) human fighter (32) What is the difference between implication symbols: $\rightarrow$ and $\Rightarrow$? I do not understand the difference between $\rightarrow$ and $\Rightarrow$. Sometimes I see implication truth tables labeled with the former, sometimes with the latter.  Aren't they synonyms of logical implication or is there any difference? How would I be able to create a grill of sorts found on the front of some computer cases such as this one CDF of absolute value of difference in random variables no Wi-Fi on Ubuntu 14.04 LTS Asus notebook with MEDIATEK MT7630e I'm new to Ubuntu. I installed it today, but the first thing I encounter is that I can only connect to the Internet through wifi.  Can someone help me?   iwconfig result :  eth0      no wireless extensions.  lo        no wireless extensions.   lspci:  00:00.0 Host bridge: Intel Corporation 3rd Gen Core processor DRAM     Controller (rev 09) 00:01.0 PCI bridge: Intel Corporation Xeon E3-1200 v2/3rd Gen Core processor PCI Express Root Port (rev 09) 00:02.0 VGA compatible controller: Intel Corporation 3rd Gen Core processor Graphics Controller (rev 09) 00:14.0 USB controller: Intel Corporation 7 Series/C210 Series Chipset Family USB xHCI Host Controller (rev 04) 00:16.0 Communication controller: Intel Corporation 7 Series/C210 Series Chipset Family MEI Controller #1 (rev 04) 00:1a.0 USB controller: Intel Corporation 7 Series/C210 Series Chipset Family USB Enhanced Host Controller #2 (rev 04) 00:1b.0 Audio device: Intel Corporation 7 Series/C210 Series Chipset Family High Definition Audio Controller (rev 04) 00:1c.0 PCI bridge: Intel Corporation 7 Series/C210 Series Chipset Family PCI Express Root Port 1 (rev c4) 00:1c.1 PCI bridge: Intel Corporation 7 Series/C210 Series Chipset Family PCI Express Root Port 2 (rev c4) 00:1c.3 PCI bridge: Intel Corporation 7 Series/C210 Series Chipset Family PCI Express Root Port 4 (rev c4) 00:1d.0 USB controller: Intel Corporation 7 Series/C210 Series Chipset Family USB Enhanced Host Controller #1 (rev 04) 00:1f.0 ISA bridge: Intel Corporation HM76 Express Chipset LPC Controller (rev 04) 00:1f.2 SATA controller: Intel Corporation 7 Series Chipset Family 6-port SATA Controller [AHCI mode] (rev 04) 00:1f.3 SMBus: Intel Corporation 7 Series/C210 Series Chipset Family SMBus Controller (rev 04) 01:00.0 3D controller: NVIDIA Corporation GF117M [GeForce 610M/710M/820M / GT 620M/625M/630M/720M] (rev a1) 03:00.0 Network controller: MEDIATEK Corp. MT7630e 802.11bgn Wireless Network Adapter 04:00.0 Unassigned class [ff00]: Realtek Semiconductor Co., Ltd. Device 5289 (rev 01) 04:00.2 Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller (rev 0a)   lspci -nnk | grep 0280 -A2:  03:00.0 Network controller [0280]: MEDIATEK Corp. MT7630e 802.11bgn Wireless Network Adapter [14c3:7630]     Subsystem: Foxconn International, Inc. Device [105b:e074] 04:00.0 Unassigned class [ff00]: Realtek Semiconductor Co., Ltd. Device [10ec:5289] (rev 01) Can I force an iPhone user to upgrade an application? I've looked through a number of the "Vote too old to be changed" questions, but I think this one's different.  I gave a downvote to an answer I thought had a critical defect, and I left a comment describing the defect. The answer was edited to satisfy my criticism, but it was done within the short grace period where edits aren't recorded as such. When I try to cancel my downvote I get the error - "Your vote is now locked in unless this answer is edited" - but it was edited!  In reference to this answer: