If an iMac has both cat-5 and WiFi connections to the world, will MacOS use them both to optimize the overall speed?  Or pick only the fastest for everything (since the ISP side of the modem is slower than Cat-5 anyway).  If yes, in what older version (if any) was this not true?  This is NOT a duplicate of any question that has two ISPs.  All devices are connected WiFi to an AirPort Extreme.  One of them is also connected by Cat-5.  I am not currently using USB or Thunderbolt or FireWire.  The Cat-5 obviously has a different IP address than the WiFi.  The Airport goes through a Motorola DOCSIS to the world.  Ookla says the wired connection downloads at 79+ MBps and the WiFi at 50+ MBps.  Also, I wasn't thinking so much of link aggregation, but like letting one app use the wire and another WiFi, giving each app more bandwidth than if they had to shared the same interface hardware.
When I'm connected to two networks with separate routers using Wifi and Ethernet, how does my Mac know what connection to use when I visit a website?
What's usually the effective visual resolution of typical Hollywood Movies? I'm really surprised by the quality of the visuals in some new movies this year (2018). I'm curious to know in what resolution these cameras typically record to experience this quality on a cinema screen? Matrices $B$ that commute with every matrix commuting with $A$ Prove by induction that $\sum_{i=1}^{2^n} \frac{1}{i} \ge 1+\frac{n}{2}, \forall n \in \mathbb N$ As the title says I need to prove the following by induction: $$\sum_{i=1}^{2^n} \frac{1}{i} \ge 1+\frac{n}{2}, \forall n \in \mathbb N$$   When trying to prove that P(n+1) is true if P(n) is, then I get that:  $$\sum_{i=1}^{2^{n+1}} \frac{1}{i} = (\sum_{i=1}^{2^n} \frac{1}{i} ) +(\sum_{i=1}^{2^n} \frac{1}{2^n+i} ) \ge 1+\frac{n}{2} + (\sum_{i=1}^{2^n} \frac{1}{2^n+i} )$$ using the inductive hypothesis. And for P(n+1) to be true it would be sufficient to prove that  $$1+\frac{n}{2} + (\sum_{i=1}^{2^n} \frac{1}{2^n+i} ) \ge 1+\frac{n+1}{2}$$  or rewriting $$\sum_{i=1}^{2^n} \frac{1}{2^n+i} \ge \frac{1}{2} $$ and here I'm a bit stuck  Thank you for your help! Is there a reason why we gain ghost reputation on the meta of an SE website? Is there any reason behind the ghost reputation we gain on the meta of a Stack Exchange site? This reputation doesn't add up to anything, but it still shows me I have gained some. Is this supposed to make any sense? Render water-paint in iOS A word for a worldly wise person who pretends to be naïve? What is a word for someone who is experienced and wise, but who deliberately acts naïve?    I don’t intend it for sarcastic use; I’m trying to describe someone succeeding in making people think that that person truly is naïve.   Is there a word for this? How do I get permissions to edit system configuration files? I can't seem to edit and save config files in the root system (eg: /etc/dhcp/dhcpd.config); it just says "permission denied" or the save option is blocked in the text editor.  I'm pretty sure I'm a root user, but how do I make sure? If I am a root user, how do I fix this? I'm trying to evaluate $(\hat{a}+\hat{a}^\dagger)^k|n\rangle$ Where $\hat{a}$ and $\hat{a}^\dagger$ are ladder operators and $|n\rangle$ the $n$th Fock state. For this, I separated the problem in three parts: $k&lt;n$, $k=n$ and $k&gt;n$. In this part I'm a bit confused: Is it possible to evaluate such operations? Some tips on how to start would be really great. How can one change the timestamp of an old commit in Git? The answers to  describe a way to amend previous commit messages that haven't yet been pushed upstream.  The new messages inherit the timestamps of the original commits.  This seems logical, but is there a way to also re-set the times? Why does the zoom sometimes stop at a point? I often find that I can zoom in to a point, but then cannot zoom any more, even when there is a lot of room to zoom to the meshes on the scene.   This is particularly annoying in the following scenario:  I often land up left clicking on the scene and the 3D cursor shifts there. I use Shift+C to shift the 3D cursor back to the origin. However, this also centers the view on the cursor and shifts the view to show all objects, and sometimes this zooms things way out &ndash; at this point, if I try to zoom in, I can zoom in to a point (using the pinch/zoom on trackpad), but then it stops zooming in.   How do I zoom in after that? Is there anything else I am doing wrong in this case? I have two questions. First, which command lists files and directories, but lists directories first?  Second question: I want to copy a list of files into a single directory, but make the target directory the first filename in the command. How to create a graph with two Y axis with different values in Excel How do you make a scatter graph with 2 Y axis (one on the left and one on the right)? I have 2 scatter graphs that I want to combine. I need to have 2 lines, both lines have the same dependent variable but have their own independent variable. Click the link "graph" below to get an idea of what I'm looking for.  (I'm using google sheets but I can also find a computer with Excel if needed) Possible Duplicate:          How do you convert a C++ string to an int?  Assume you are expecting the string to have actual numbers in it ("1", "345", "38944", for example).  Also, let's assume you don't have boost, and you really want to do it the C++ way, not the crufty old C way. I have made a raster elevation map of Greenland, and have information of the region, cities and more as vectors. The information is not in the same place as my elevation map.  I have selected EPSG:5938 on the bottom right in QGIS and on my informations and elevation map I have set the CRS to the same like the picture    How do I get it all on the same position? How to extend WIFI from ethernet Here's my current setup.   Bonded "Zone" DSL modem/router on main level serving laptop #1 via Ethernet and laptop #2 via WIFI.  WIFI does not serve basement level well, so I have Ethernet running to basement where it is divided by a switch with one Ethernet going to laptop #3 and another Ethernet going to entertainment system, which houses a Sony Playstation 3. The PS3 has gone on the fritz and is now only good for playing discs, so I recently added a Google Chromecast to the TV. The Chromecast, of course is WIFI only, and is only receiving a weak signal. Plus I need to have a decent WIFI signal to my phone, which is the interface device for the Chromecast. So what I would like to do is to use the Ethernet that was serving the PS3 and broadcast WIFI from it. What device can I plug the Ethernet into that will do this for me? And if you have a recommendation, are there any special setup instructions? Prove: If a sequence converges, then every subsequence converges to the same limit. I need some help understanding this proof:  Prove: If a sequence converges, then every subsequence converges to the same limit.  Proof:  Let $s_{n_k}$ denote a subsequence of $s_n$. Note that $n_k \geq k$ for all $k$. This easy to prove by induction: in fact, $n_1 \geq 1$ and $n_k \geq k$ implies $n_{k+1} &gt; n_k \geq k$ and hence $n_{k+1} \geq k+1$.  Let $\lim s_n = s$ and let $\epsilon &gt; 0$. There exists $N$ so that $n&gt;N$ implies $|s_n - s| &lt; \epsilon$. Now $k &gt; N \implies n_k &gt; N \implies |s_{n_k} - s| &lt; \epsilon$.   Therefore: $\lim_{k \to \infty} s_{n_k} = s$.   What is the intuition that each subsequence will converge to the same limit I do not understand the induction that claims $n_k \geq k$ What do the fields in ls -al output mean? How can I convert a node made material into an image texture? I have a sphere having a planet material MADE WITH NODES, and I want to convert this material into an image texture; because this material is made with nodes and only works in Blender, but I want to use in another software. This is my sphere material :   For Example : This is Jupiter :  And this is the texture :  In this case I used a downloaded image for Jupiter to be the material but I want the opposite, I want to change the material to image texture Like The shape of Jupiter texture. Is there anyway in Blender that can achieve my goal ? This is the file with my sphere material .  Textures Needed :  Albedo / Color / Diffuse Normal Map Roughness Glossines  I am using normal nodes and I am not useing the new Principled-shader Is there a way to rename (or do away with the name of) the bibliography page that is output using BibTeX?  If so, is the name dependent on the bibliographystyle, or is it something inherent within the BibTeX functionality? $X/{\sim}$ is Hausdorff if and only if $\sim$ is closed in $X \times X$ $X$ is a Hausdorff space and $\sim$ is an equivalence relation.  If the quotient map is open, then $X/{\sim}$ is a Hausdorff space if and only if $\sim$ is a closed subset of the product space $X \times X$.  Necessity is obvious, but I don't know how to prove the other side. That is, $\sim$ is a closed subset of the product space $X \times X$ $\Rightarrow$ $X/{\sim}$ is a Hausdorff space. Any advices and comments will be appreciated.