Is the spectrum of visible light infinitely divisible? I assume the question pertains to electromagnetic waves in general, but I am at the moment interested in visible light. Our capacity -- both human and device -- for discerning wavelengths of light is limited. But is the spectrum really continuous and is it also practically so (ie. which are the objects that actually emit an infinite compendium of wavelengths of visible light)? For example, assuming a wave with wavelength of 500 nm, can you have a wave with wavelength 500,123456 nm [of course you can], and can you just go on and on (assuming you have equipment sensitive enough to measure it) to measure waves with wavelengths of, say, 500,123123123123123123123123123123123123123123123123 nm wavelength, or does this break down at some point (barring sensitivity of measuring equipment)? I looked at some questions, like:  but that didn't seem to answer my question.
Is there an infinite amount of wavelengths of light? Is the EM spectrum continuous? The electromagnetic spectrum is a continuum of wavelengths of light, and we have labels for some ranges of these and numerical measurements for many.  Question: Is the EM spectrum continuous such that between two given wavelengths (e.g. 200nm and 201nm) there is an infinite number of distincts wavelengths of light?  Or is there some cut-off of precision with which light might exist (e.g. can light only have wavelengths of whole number when measured in nanometers, etc.)?
The set of convergent points of a sequence of continuous functions is Borel Suppose that $f_n$ are continuous.  Prove that $E=\{x\in \mathbb{R}:f_n(x)\text{ is convergent}\}$ is Borel.   My first instinct is to take balls around $\lim_{n\to\infty}f_n(x)$, for each $x$ in $E$, and then show that there has to be some ball small enough so that everything inside that ball is a member of $E$. But this would imply not only that $E$ is Borel, but moreover that it is open, so I don't think that can be right.  Can someone show me how to do this? How to tweet using terminal? Why are properties lost in the Cayley–Dickson construction? Motivating question:    I'm aware that one can construct a hierarchy of number systems via the Cayley–Dickson process:  $$\mathbb{R} \subset \mathbb{C} \subset \mathbb{H} \subset \mathbb{O} \subset \mathbb{S} \subset \ldots $$  "Reals" $\subset$ "Complex" $\subset$ "Quaternions" $\subset$ "Octonions" $\subset$ "Sedenions" $\subset$ $\ldots$  and that at each step you're given a multiplication table that tell how the elements interact. As you move up the ladder, certain "nice" properties are lost: ordering,  commutativity, associativity, multiplicative normedness, etc... Given the multiplication table, you can show that these properties don't hold.   Eric Naslund noted that "the first 4 are very special as they are the unique 4 normed division algebras over ℝ", no surprise then that these $2^n$-ions have found quite a bit of use. I'm interested in the sequence itself however, irrespective of how useful a $2^{256}$-ion might be (ducenti-quinquaginta-sex-ion?).   I feel like something deeper is going on here though that I don't understand. Why are these particular properties lost at each step? Is it possible to quantify the process such that, at the $2^n$-ion you can say something about the symmetry of the multiplication table*?  * I'm making an ansatz that there is a connection between the symmetry of the multiplication table and these "nice" properties. How can I cancel an edit I made on another user's question or answer? Edits made by users who do not have edit privileges are placed in a queue until it is peer reviewed.  E.g., I edited someone else's answer. but changed my mind. If I'd edited my own question/answer, there would be a "Rollback" button, but there's no such button in the scenario I'm describing (at least none that I can see).  This is more relevant today because users can only have at most five edits waiting in the queue, and allowing one to cancel an edit would permit them to free up one of their five pending edits for something else.  Is there a way to remove one's edit from the peer review queue? Update on Ubuntu - coloured lines around everything Everyday I check for updates on Ubuntu 16.04 LTS. I updated to 4.4.0-65-generic today and now on everything I'm getting thick rainbow coloured lines around every dialog box in every program. My setup is pretty standard. Skylake i5-6500, Nvidia 950gtx. Does anyone know how to fix it? I need help with a specific command that I am using in a new game that I am creating inside of Minecraft. The command is:  /give @p sign 1 0 {BlockEntityTag:{Text1:"{"text":" [MF2]","color":"gold","clickEvent": {"action":"run_command","value":"tellraw @a [""{"text":"[MF2]  ","color":"gold"},{"selector":"@p","color":"dark_aqua"},{"text":" is now an admin of the server!","color":"white"}]"}}",Text3:"{"text":"Click to join Admin","color":"dark_aqua","clickEvent": {"action":"run_command","value":"scoreboard teams join admin @p"}}"},display: {Name:"Custom Sign"}}   If I take out the /tellraw command then the command works fine, but I need the command in there to announce to the game that a new admin has joined.  With the tellraw command, the error message is the following:  Data tag parsing failed: Unexpected token 't' at: text":" [MF2]","color":"gold","clickEvent":{"action":"run_command","value":"tellraw @a [""{"text":"[MF2] ","color":"gold"}, {"selector":"@p","color":"dark_aqua"},{"text":" is now an admin  of the server!","color":"white"}]"}}",Text3:"{"text":"Click to join Admin","color":"dark_aqua","clickEvent": {"action":"run_command","value":"scoreboard teams join admin @p"}}"   If anyone knows how to fix this, please let me know. pattern matching in vim Why isn't this sudo mv operation with wildcard working? How to call shell commands from Ruby How do I call shell commands from inside of a Ruby program? How do I then get output from these commands back into Ruby? Why can't I seem to grasp interfaces? Could someone please demystify interfaces for me or point me to some good examples? I keep seeing interfaces popup here and there, but I haven't ever really been exposed to good explanations of interfaces or when to use them.  I am talking about interfaces in a context of interfaces vs. abstract classes. How can I install the Social-Engineering Toolkit (SET)? There is this software (SET) from Backtack 5 source that I found out about. But I don't know how to install this thing. Could somebody help me?  Here the link: 408 Request Time-outs still continues I'm frequently getting 408 Request Time-out errors  when browsing through Stack Overflow and Meta. I used to get this four or five times a day before, but now it has become very frequent. I've read  in which Kyle Brandt ♦ says:     We send our web logs to SQL so we can query them. It turns out that we have a bug that prevents 408s from being logged to SQL. [...] I will do more extensive research when our 408s are part of queryable logs (should be a week or two [...]).   My internet connection is somewhat stable and I haven't experienced this issue on other sites before. I don't think it's a browser-specific issue as it is reproducible on latest versions of Google Chrome and Firefox (on Ubuntu 13.10). However, it is specific to Stack Overflow and Meta. I'm unable to reproduce this on other SE sites.  Am I the only one facing this issue? Could it be something wrong with the regional CDN or something like that? Could someone please take a look at this issue? ()  This appears when I try to close-vote questions, too: A Variation of the even-town odd-town problem Let assume facebook has $n$ users. Mark Zuckerberg decided that people are allowed to open groups under the following restrictions:      1) No two different groups can exactly the same participants.      2) The number of users in each group is even.      3) Every two group has an odd number of common users.      Denote by $m$ the maximal number of groups that can be formed in facebook under the restrictions mentioned above. Prove $m \leq n$.   I tried solving this by defined a matrix, multiplying it by its transpose and using some rank considerations I thought I could derive the bound, but I didn't succeed. Could you please give me a hint?  The question had anther subsection : prove that in the case that $n$ is even than we have stron inequality What happens when you run out of movement while jumping? Maybe a stupid question but how can I tell if I have a static IP address or a dynamic IP address? Running Fedora-13 "This is a favorite question" tooltip when not favorite What is the spell save DC and spellcasting modifier for a Rogue with Magic Initiate? As a rogue I'm planning to take Magic Initiate with warlock class. The Magic Initiate feat says:     [...] Your spellcasting ability for these spells depends on the class you   chose: Charisma for warlock [...]    cantrip 1: Booming blade or Green flame blade cantrip 2: Minor illusion 1st-level spell: Hex    My stats bonuses are: STR : -3 | DEX +6 | INT 0 | WIS +1 | CHA +4 | prof : 4  Questions:   Green flame blade :      [...] The second creature takes fire damage equal to your spellcasting   modifier. [...]   What is my spellcasting modifier? 0 from INT as rogue or +4 from CHA as warlock?   Minor illusion :      [...] If a creature uses its action to examine the sound or image, the   creature can determine that it is an illusion with a successful   Intelligence (Investigation) check against your spell save DC. [...]   What is my spell save DC? 12 (8 + 0 from INT + 4 from prof) or 16 (8 + 4 from CHA + 4 from prof)? What other languages have features and/or libraries similar to Perl's format? Why does my user number show up in the search box when clicking my profile information? How to set edge bevel weights from a python script I need to set weights for some edges from a python script. I have tried looping through object.data.edges and setting bevel_weight values but I can't get it right. It only works if I have first edited some edge's bevel weight by hand from the 3d-view's transform window. But I would like to get it work from my script without any manual hacking.  Steps to reproduce:  Start Blender with default cube and switch to Scripting view.  Try to set weights for all edges:  for edge in C.object.data.edges:     edge.bevel_weight = 1.0   Verify that values changed:  for edge in C.object.data.edges:     edge.bevel_weight   Switch into edit mode in 3d-view and open up transform window by pressing n. Select edges to see that the change did not work (bevel weights are all zero). Switch back to object mode and read values again in scripting console to see that they were reset to zero:  for edge in C.object.data.edges:     edge.bevel_weight   Go back to edit mode and change some edge bevel weight straight from the transform window by hand. Go back to object mode and change values again from the scripting console:  for edge in C.object.data.edges:     edge.bevel_weight = 1.0   This time it works, bevel weights are 1.0 when you go back to edit mode and look from the transform window.   Any ideas? My final need is to apply a bevel modifier to only some set of edges and that's why I'm trying to mark them by using weights. Using vertex group for bevel modifier does not work in my situation, since I need to specify edges, not vertices, which to bevel.   I'm using Blender v2.71.