i have a simple question for you, i need to "merge" 2 parts of the same object in edit mode where the faces collide, here a simple example to better explain the desiderata:   IS it possible in Blender with a simple operation? or do i have to recreate the whole parts to make them collide correctly?
I'm trying to find a simple way to create vertices where two objects intersect and delete the leftover internal planes + then join the meshes so that I have one hollow mesh to sculpt. The reason I need to know this is that on my first sculpt I just joined the meshes, but it didn't create vertices at the intersecting points so when I went to sculpt it just overlapped the meshes as you can see here in the neck.  Here is what I am working on now, it needs to be 1 hollow mesh
Topologist's sine curve is connected I just came across the example of the topologist's sine curve that is connected but not path-connected. The rigorous proof of the non-path-connectedness can be found .   But how can I prove that the curve is connected? To be honest, even intuitively I am not being able to see that the curve is connected. I am thinking if it is proved that the limit point of $\sin(1/x)$ as $x \to 0=0$, then it would be proved. But, why is this true? IMO, this limit doesn't exist. Intuitively also, it seems that the graph would behave crazily and not approach a particular value as a tends to $0.$  EDIT (Brett Frankel): There are a few different working definitions of the topologist's since curve. For the sake of clarity/consistency, I have copied below the definition used in the linked post: $$ y(x) = \begin{cases} \sin\left(\frac{1}{x}\right) &amp; \mbox{if $0\lt x \lt 1$,}\\\ 0 &amp; \mbox{if $x=0$,}\end{cases}$$ I've got a utility that outputs a list of files required by a game.  How can I run that utility within a C program and grab its output so I can act on it within the same program? UPDATE: Good call on the lack of information.  The utility spits out a series of strings, and this is supposed to be portable across Mac/Windows/Linux.  Please note, I'm looking for a programmatic way to execute the utility and retain its output (which goes to stdout). Random operators Let $(\Omega, \mathcal F,P)$ be a probability spaces and $H$ be a Hilbert space. By a random operator $A$ from $H$ to $H$ we mean a linear continuous mapping from $H$ into the Frechet space $L_0^H (\Omega, \mathcal F,P)$ of all $H$-valued random variables. My question is: How Can we define $|A|$ and the adjoint $A^*$? Can the graph of a bounded function ever have an unbounded derivative? I was coding a physics simulation, and noticed that I was using discrete time. That is, there was an update mechanism advancing the simulation for a fixed amount of time repeatedly, emulating a changing system.  I though that was interesting, and now believe the real world must behave just like my program does. It is actually advancing forward in tiny but discrete time intervals? Why does this CSS margin-top style not work? How to prove that $L=${$a^p$: p is prime} isn't regular? I tried using pumping lemma or finding infinite equivalence classes, but I didn't succeed.  It's clear to me that there is no automata that accepts this language, but I just can't formally prove that this language isn't regular.  How can you prove it? Rounding Percentages Let $E|F$ be an algebraic field extension and a ring $K$ such that $F\subseteq K\subseteq E$. It is true that $K$ is a field? I know how to define a package or a class, but how do I make it available (to myself) at all times?  Say I have the package file commonstuff.sty (or myprettyclass.cls), that I want to be able to include in any .tex file I create on my computer. Where do I put it? Do I need to run some installer on it, or is it enough to keep it in a certain folder?  Note: I know I can just place it in the same folder as the .tex file, but that's not what I'm after here. I'm looking for a way to "install" the package centrally on my computer. What do I use on linux to make a python program executable What is a disputed flag? In my flagging summary under the statistics, there is 1 flag listed as "disputed".  This is the first time I've ever seen a disputed flag in my summary, so I'm just curious, what is a disputed flag? How would you even dispute a flag? Is this the same as voting a flag as invalid? $f,\overline f$ are both analytic in a domain $\Omega$ then $f$ is constant? is it true if $f,\overline f$ are both analytic in a domain $\Omega$ then $f$ is constant? I am not able to  find out what property of holomorphic map I need to apply. please help.Thank you.  $f(z)=u(x,y)+iv(x,y)$, $\bar{f}(z)=u(x,y)-iv(x,y)$ Changing background color to transparent in GeoServer? How to set the background color to transparent. I want use style which describe in *.sld file for all my photo with tif format. How to do that? See a list of my top voted comments? Or another way to track progress on Pundit? Pundit  Left 10 comments with score of 5 or more   I saw a discussion question that mentioned Pundit, which that stated that , however, something like top voted comments seems to fit in with the rest of stackoverflows feature set, as well as indirectly provide a method to track progress on this badge. Should there be (or is there already) a list of my top voted comments somewhere? Word to describe using sarcasm or a similar approach to lead someone to recognise their own mistake Seeing as C# can't switch on a Type (which I gather wasn't added as a special case because is relationships mean that more than one distinct case might apply), is there a better way to simulate switching on type other than this?  void Foo(object o) {     if (o is A)     {         ((A)o).Hop();     }     else if (o is B)     {         ((B)o).Skip();     }     else     {         throw new ArgumentException("Unexpected type: " + o.GetType());     } } Why are badges on per-site-metas separate? Badges earned on per-site meta sites are separate from the main site, but reputation is carried over from the main site (because you don't earn any on Meta).   I perfectly understand keeping the rep the way it is (meta votes are too subjective to integrate them with rep) but the badge split seems odd to me.  Multiple badges are in fact impossible on Meta; Mortarboard, Bounty related badges. In addition badges in general are much harder to earn due to the lower amount of users and content; badges like Great Answer are nearly impossible.   As a result of this, most users on Meta end up with the easy 5-10 bronze badges for basic participation on Meta and not much else; stuff like Supporter and Critic that are hard not to get.   I understand the want to drive more people to meta, so perhaps badges are separate to institute a reward system; however this doesn't seem to work well since Meta badges (mostly) don't appear on the main site. This in combination of the 0 rep gain makes Meta feel almost not real. It also makes part of your progress (badges) on the main site invisible on Meta, and vise versa.  IMO the badges should be the same on both Meta and main site, but more Meta-oriented badges should be added to encourage use of Meta. This way Meta badges feel "real" instead of "Meta".  Is there an official reason for per site metas having separate badges? Why can't I import "pygtk" with Python 3.2 from PyDev? Solving the Kolmogorov forward equation for transition probabilities Let $\lambda \mu &gt; 0$ and let $X$ be a Markov chain on $\{1,2\}$ with generators  $$ Q = \begin{pmatrix} -\mu &amp; \mu \\ \lambda &amp; -\lambda \end{pmatrix}$$  Write down the forward equations and solve them fro the transition probabilities, $p_{i,j}(t), i,j = 1, 2$.  The answers say:  "We have that   $$p_{11}' = -\mu p_{11} + \lambda p_{12}, \, \, \, p_{22}' = -\lambda p_{22} + \mu p_{21}$$  where $p_{12} = 1 - p_{11}$ and $p_{21} = 1 - p_{22}$. Solve these subject to $p_{ij}(t) = \delta_{ij}$, the Kronecker delta, to obtain that the matrix $P_t = \{p_{ij}(t)\}$."  The bits I don't understand are these  1) How do they get those equations in the first place? For example, why have they added $\lambda p_{12}$ when the coefficient for $p_{12} = \mu$?  2) How do you solve these equations? What do you do with that Kronecker delta to solve them?