Continous periodic function is uniformly continuous? $f:\mathbb{R}\rightarrow\mathbb{R}$ be a continuous function such that $f(x+1)=f(x)\forall x$ we need to show $f$ is uniformly continuous function.  please give me some hint:
How do I show that all continuous periodic functions are bounded and uniform continuous? A function $f:\mathbb{R}\to \mathbb{R}$ is periodic if there exits $p&gt;0$ such that $f(x+P)=f(x)$ for all $x\in \mathbb{R}$. Show that every continuous periodic function is bounded and uniformly continuous.   For boundedness, I first tried to show that since the a periodic function is continuous, it is continuous for the closed interval $[x_0,x_0+P]$. I know that there is a theorem saying that if it is continuous on a closed interval, then it is bounded. However, I'm not allowed to state that theorem directly. Should I just aim for a contradiction by supposing f is not bounded on the interval stated above?
How to prove that you have significant ties with family in your home country? How can I prove the immigrant officers that I have significant ties in my home country?  Are there any documents that I need? Add a custom curve mapping property for an add-on? Question The title says it all. I want to be able to make this in Blender's UI, and sample it at specific points :  Problem There is very insufficient documentation on this, and I can't find any examples for how to create a . I have worked with templates before, and , but it requires a curve mapping prop. Extra Info I found a few threads about this, and one gives me the impression that this cannot be done at all, but it is also very old.   This similar question has been asked here before, but it didn't even get a comment:  Is this even possible to access in python (as in only accessible in C)? Evaluate the following limit of finite sum Including +/- signs to battery in Circuitikz I'm attempting to draw a battery (using the battery1 component) that includes positive and negative signs at the appropriate ends. A  that was answered here (using version 2.4) shows exactly what I mean:    Only, of course, I want to be using a battery1 symbol instead. So, I have my code as follows:  \usepackage[americanvoltages,fulldiodes,siunitx]{circuitikz} \begin{document} \begin{circuitikz}     \draw (0,0) to [battery1=\SI{9}{V}] (3,0)                 to [pC,v=$v_C$] (6,0); \end{circuitikz} \end{document}   And I end up with this:    Notice the lack of +/- signs (I know how circuits work so I don't need to be actually shown these signs, but for the sake of copying my class notes diagrams I want these signs to be included in my latex diagram).  In either case, I think it may have something to do with the version of Circuitikz I'm using because I'm using the latest version (I believe, 0.3.0) but in the previous question linked above, they were using 2.4 and it worked out for them.  I would really like to find a way to add +/- without having to manually add it with Tikz or something, i.e. just have it naturally part of the component without having to add nodes or extra Tikz code etc. If that's not possible, then I'll have to settle for that as a last result.   Thank you for your help!  EDIT: I should also mention that I've tried using battery1, v=$9V$ instead of battery1=\SI{9}{V} and to no avail (the +/- signs still don't show up). Session_ID_Remove Issue in API callouts in Salesforce Is there a quicker way to turn on WiFi Hotspot? is there a way to automate (or at least reduce the number of steps) to turn on or turn off the WiFi hotspot on my Galaxy 3.  I have to    unlock  press the menu button  press settings press More Settings Tethering and portable hotspot Slide portable hotspot on. single query to print all the rows whose count is greater than 10 Residue fields of schemes of finite type (over $\mathbb{Z}$) Suppose $X$ is a scheme of finite type over $\mathbb Z$. I want to prove that:  (1) The residue fields of closed points of $X$ are finite;  (2) For a given $q=p^n$ with $p$ prime, there is only a finite number of closed points of $X$ whose residue field is $\mathbb F_q$.  For (1), I see that one has to use some form of Nullstellensatz. First, we suppose $X=\operatorname{Spec}(A)$ affine, and $A=\mathbb{Z}[X_1,...,X_n]/I$. We need to show that if $m$ a maximal ideal of $A$, then $A/m$ is finite. Note $p=\mathbb Z\cap m$. If $p$ is maximal, we get that $A/m$ is of finite type over $\mathbb F_p$ thus a finite extension by Nullstellensatz and we are done. But $p$ could be the $(0)$ ideal in which case I neither conclude nor get a contradiction.  For (2), we can again argue locally, so we need to show that $A$ contains only a finite number of maximal ideals $m$ with $A/m$ of fixed cardinality $q=p^n$. I get an impression that to count these ideals its the same as to count the number of automorphisms of $\mathbb{F}_{q}$ which fix $\mathbb F_p$, but the corrspondence is not bijective, so we only get an upper bound which is enough. Is this idea correct? Doesn't Matlab work on ubuntu 16.04? In normal line integration, from what I understand, you are measuring the area underneath $f(x,y)$ along a curve in the $x\text{-}y$ plane from point $a$ to point $b$.  But what is being measured with complex line integration, when you go from a point $z_1$ to a point $z_2$ in the complex plane?  With regular line integration I can see $f(x,y)$ maps $(x,y)$ to a point on the $z$ axis directly above above/below $(x,y)$.  But in the complex case, when you map from the domain $Z$ to the image $W$, you are mapping from $\mathbb{R^2}$ to $\mathbb{R^2}$ ...it is not mapping a point to 'directly above/below'...so I don't have any intuition of what is happening with complex line integration. I understand when we say current, we mean charge (protons/electrons) passing past a point per second. And the charges have energy due to the e.m.f. of the power supply.  Now tell me, if a lamp has resistance and you hook it in the circuit, how will the current stay the same? The charges obviously lose energy in the lamp and so become SLOWER, which should mean current decreases, right?  [Edit] All answers explained a bit of everything, so it was hard to choose one. If YOU are looking for an answer, please check the others too, in case the accepted one doesn't answer your question. Assume  $$G_1=\mathbb Z_5 \times \mathbb Z_{5^2}\times \mathbb Z_{5^3}\times \mathbb Z_{5^4} \times\ldots$$ $$G_2= \mathbb Z_{5^2}\times \mathbb Z_{5^3}\times \mathbb Z_{5^4} \times \ldots$$ How do I prove $G_1$ and $G_2$ aren't isomorphic? I asked  this question here  and I received tree answer, but the answer of Ludolila will be complete when  $G_1$ and $G_2$ are not isomorphic.    Thanks in advance Proof that Conditional of Poisson distribution is Binomial Imported 3D scan displays texture in editor, but renders without texture I am new to blender and I have a 3D scan of a stone tablet (which I am unfortunately not able to share, so I will try to be as detailed as possible) which was imported as OBJ and MTL files.  The editor displays the texture and mesh perfectly, but when I render the scene (pressing F12) the texture is not there.  I am trying to use blender to reduce the file size of the tablet for use in a three.js visualizer for a website.  I have tried exporting the file as a JSON file (as well as several other file formats to the same effect) for use in my three.js webapp and thought it was an issue with three.js, but after seeing that blender did not render the tablet with the texture I now believe it is an issue with my blender configuration. I am unable to find within blender or online any way to check what current resources I have displayed and what options I have with them.  I have not applied a mesh or texture to the object, but when I do so it renders with the generated texture applied in the default pink.  I am confused as to where the disconnect is between the editor and the renderer. I am still figuring out what is important and where to find all the relevant information, so any help on that regard would be very much appreciated.  Here is what blender looks like for me with the sensitive parts censored (can't be too careful these days):   I have looked at this question:  And there is no material overwriting the texture - I have not assigned a material to the tablet at all. EDIT: In regards to the duplicate answer, I looked at that one as well and the issue I have is that it doesn't have an actual texture file that I can just put on it.  The OBJ MTL files come with their own file that can't be applied directly to the model.  Blender read the OBJ MTL files and recreated the object inside blender algorithmically - and now I need to know how to get blender to tell me where that texture is and how I can get it to show up in the render.  The texture is not on my hard drive, but entirely within blender which is the issue I am having. Why was Sam Wilson chosen for this, but not Bucky? At the end of the Avengers: Endgame movie,      old Steve Rogers passed down his mantle of Captain America   to Sam Wilson.  Why didn't he choose Bucky for this? Bucky seems more fit for the job as he is a super soldier. Non constant analytic function from $\{z\in\mathbb{C}:z\neq 0\}$ to $\{z\in\mathbb{C}:|z|>1\}.$ Are there good reasons why it's a better practice to have only one return statement in a function?   Or is it okay to return from a function as soon as it is logically correct to do so, meaning there may be many return statements in the function? I am trying to convince my friend that the integral of $0$ is $C$, where $C$ is an arbitrary constant. He can't seem to grasp this concept. Can you guys help me out here? He keeps saying it is $0$. Why is it so difficult to pull an immersed mug out of the water? Suppose I put a mug in the water and then tilt it so that the water gets inside. It then floats due to buoyant force. But if I try to pull it out then a lot of force is needed. That's due to suction? What exactly happens at the moment when the force I apply is enough to pull the mug out? And what causes the loud pop sound when that happens? Calculating peaks in DEM using GRASS