How can we be sure that there are only four dimensions?
How to prove that we are living in a 3+1D world?
The exercise is: Prove that $-(-v)=v$ for every $v \in V$  Proof Suppose  $v \in V$ and $V$ is a vector space. Then $-(-v) \in V$ as result of the scalar multiplication property and $-(-v)=-(-1\cdot v)=-1 \cdot(-1\cdot v) =(-1 \cdot-1)\cdot v = 1 \cdot v = v $ The desired result $-(-v)=v$ holds.  The solution manual gives the proof:  Proof   I just wanted to make sure that the way I did the proof isn't missing anything?Thanks Is there a way to force the iPhone to use its own microphone when connected to a Bluetooth speaker? I connect my phone to a Bluetooth speaker to play music. When engage Siri or try to use dictation, the phone wants to use the microphone on the Bluetooth device, which is either too crappy or too far away for it to understand what I am saying.  So, I would like a way to restrict the iPhone to using its own microphone even when connected to a Bluetooth speaker.  I am open to doing this via a setting, buying an app, or jailbreaking or whatever.  Is there a way to do this? Increment Record based on field Living potato clock? Travel duration from Earth to a star at 9.8 m/s² acceleration How can one cite theorems of references? I would like to cite the item (iii) of proposition 3 of a reference. How can I do it? Which ways do you suggest? This is a question not only about LaTeX, but also about style. One option I have seen to cite pages of a reference is \cite[p.~333]{Audet}. Is there something similar to cite theorems, propositions and so on? Update Manager doesn't ask for a password Oneiric update manager no longer asks for a password to update already installed software.  This is a change in behavior from previous versions.  Is there a way to revert this behavior and get the Update Manager in Oneiric to ask for a password again?  Thanks! HD bad blocks: is there a way to repair them? My child has chickenpox, am I infectious? My 3-year-old has had chickenpox for about 2-3 days, but a close friend has just had a baby and I want to go and help. Is it possible that I am infectious, despite not having the illness? I had it as a child, so (hopefully) can't actually get it myself. Thanks! How well does T-Mobile's (US) Simple Choice plan work when in Europe? Can anybody explain about real linear space and complex linear space? This is definition      "A real linear $V$ is said to have an inner product if for each pair of elements $x$ and $y$ in $V$, there corresponds a unique real number $(x.y)$ satisfying what we know as axioms for inner product."    What does it mean? $(x.y)=xy$ and $xy$ is a real number?   When $(x.y)$ is complex, it is called complex space, does that mean that $(x.y)=xy=$ complex?   I don't understand what inner product is. How to prove that a limit does not exist? Let $x \in \mathbb{R}$ and let $\lfloor y\rfloor$ be the largest integer less than or equal to $x$. $$ f(x) = \frac{1}{x} - \left\lfloor\frac{1}{x}\right\rfloor$$ How does one prove that the $ \lim_{x\to 0} f(x)$ does not exist by using a Epsilon Delta proof? There is a hint given that you can use a proof by contradiction. Can we build capacitors on a PCB board? This seems to be quite a trivial problem, but after some searching I can't stil figure out the answer. One can run tcpdump using "any" as the interface description, ie:   # tcpdump -i any -n host 192.168.0.1   Is there any way to force tcpdump to show on which interface displayed packet was captured?  Update:  As more people confirmed this is probably not possible with vanilla tcpdump, can someone propose a solution to mentioned problem? Perhaps different sniffer?   General issue is as follows: On a system with 50 interfaces determine what is inbound interface for packets coming from specific ip address. How to get the CPU cycle count in x86_64 from C++? How can I get list of symbols, abbreviations, abstract, acknowledgements into Table of Contents before Introduction, and under roman numerals? Top bar search doesn't pick up subdomains I wanted to switch to  in the handy dandy site switcher in the new top bar. Entering "cook" brings up nothing:     ... so I have to remember that the boutique title of the site is "Seasoned Advice":     ... in which case the site switcher also thinks that maybe I was thinking of heading over to  to see what's up. So the site switcher searches site names and descriptions, but not subdomains. This is unexpected behavior - I believe it should search all three. Are there any reserved words in SQLite? I see these two expressions are used almost identically in different contexts. Is there a difference between I have got and I have gotten? What may happen after a stack of spells resolves? Within the same phase, once a stack of spells has resolved in its entirety, is priority once again given to a player so that more spells may be cast?  For example:  I attack with a creature. Opponent opts not to block. Now, I want to buff (e.g. +3/+3) my creature multiple times, but I'm afraid of my opponent responding with a burn (e.g. Deal 3 damage) spell at the top of the stack. Can I buff once, ask if opponent wants to respond, then allow the stack to resolve. Then, in the same phase, cast more buff?