This is a follow-up question to .  Does there exist an example of a bounded and continuous but not necessarily uniformly continuous function defined on all of $\mathbb{R}$, which is not H\"{o}lder continuous?
Can someone give me an example of a function $f: I\to \mathbb R$ which is uniform continuous but not Hölder continuous (for any $\alpha$)? Here $I$ is an interval. If $I$ is closed and bounded then we are essentially assuming that $f$ is merely continuous.   By saying that $f$ is not Hölder continuous for any $\alpha$, I mean for all $\alpha &gt;0$,   $$\sup_{x,y\in I, x\neq y} \frac{|f(x) - f(y)|}{|x-y|^\alpha} = \infty.$$  That is, I need to find a function $f$ so that for all $\alpha$ and $M&gt;0$, there are $x, y\in I$ so that   $$ \frac{|f(x) - f(y)|}{|x-y|^\alpha} \ge M.$$  I know that $f(x) = x^\alpha$ are $\alpha$-Hölder continuous. Thus, in some sense, I am looking for $f$ which are worst than the functions $x^\alpha$ for all $\alpha &gt;0$.
Fighter War Magic, Using Booming Blade / GFB If my Fighter (Eldritch Knight) use War Magic (PHB p. 75) to use the cantrip Booming Blade, will I be able to use my Extra Attack, and bonus action attack, to make 3 attacks at level 7? Privacy/Security concers for setting up business email using Gmail app on Nexus devices I need to set up my business email*(non gmail email)* on the mobile devices (Nexus 5 and Nexus7). The business has its own private mail server. The way I can do it is by using Gmail app on these devices. The question I have is does Gmail app on the mobile devices store the IMAP emails(non gmail emails) on the gmail servers? Or Gmail app is just a client and does not bother storing the IMAP emails(non gmail emails) on its servers that are not gmail emails? Thanks for the insight... I have installed VirtualBox OSE on Ubuntu 11.04 and Windows XP pro as the virtual machine. Now I want to have a shared folder which can be accessed on both, my host Ubuntu machine, and my WinXP guest virtual machine.  How can I do that? Editing LaTeX generated PDF Is there an application (in Windows, Unix, or Mac) that allows you to edit the LaTeX generated PDF. I know there is pdfsync, but it only gives you the line, and then you have to search where in the line you want to make the change. This is OK sometimes, for a couple of changes, but when there are lots of changes it becomes really tedious.  I would really like to accelerate this process of correcting mistakes (mostly grammar, missing commas etc.). in my document, without going through all the markup. I'm including \usepackage{hyperref} so that each instance of \ref (as well as each page number in the index and the table of contents) automatically links to that page.  When I'm viewing the document (in ) and I click a link, I jump to the linked page.  Is there any easy way to go "back" to where I was before I clicked the link?  (And is the answer any different when using Adobe Acrobat reader?) What is a reasonable sample size for correlation analysis for both overall and sub-group analyses? I am running Pearson's correlation on an overall sample of 400 respondents.   When I isolate male and female responses, my sample becomes 220 male responses and 180 female responses.   If I further isolate male and female responses by (say) age groups, some sample sizes become as low as 35 responses (for example, for females over the age of 65).  My question: How good are these sample sizes for correlation analysis? (I am looking at the relationship between income levels and overseas travel.)   (I think this has something to do with margin of error but how does this apply to inferential analysis which is based on probability. I can understand its role in descriptive statistics such as results of a political poll). 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I have a number of DIV's that break up a page into logical elements for styles and positioning, etc.  As part of optimizing my site for search engine spiders, should I include a title attribute within these DIV's?  (Yes I have a title as part of the whole page, I'm curious on individual structual elements)  Ex  ... &lt;div id="SearchOptions" title="Search filters and options - Type in a name or pick a business and Click 'Search' to get started" &gt;   .... &lt;/div&gt; ... Arrays in Java and how they are stored in memory I made a series of outdoor shots with Nikon D5000, with the 18-55mm 1:3.5-5.6G VR kit lens.  On some shots, I see in the EXIF info f/11, and in another shot, f/9.    How can that be, that the f-number is greater than 5.6, when that's listed as the maximum in the lens spec? Favorite questions in the Android app How to run scripts every 5 seconds? I have a script that needs to be run every five seconds. I know that cron can do tasks by the minute, but is there a way to run something every second? Optimal tiling of polygon using ArcGIS Desktop? I am trying to tile a polygon with a minimal number of fixed sized squares.  Currently I am creating a fishnet over my polygon then spatially joining the squares that intersect the polygon. This is not optimal.  Also note the squares can be shifted vertically/horizontally but not rotated.  My end goal: The polygon represents a clipped image and I want a tiling of the clipped image. Where each tile is 300px by 300px. Some overlap is fine if that makes the problem easier.  Current    Manually optimized    Are there any tools or algorithms that would help with this? I am proficient with Python and ArcMap.  The polygon was created from line features so I also have access to those segments. Maybe that would will help for generating the squares.  The entire polygon must be covered. How to handle client requests to violate copyrights? What are the uses of "using" in C#? I saw a video where the person copied a material from one object to another (Cycles).  How can I accomplish this?