Playing sound files with Java - Error: Could not find or load main class [Classname]
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Let $a, b, \&amp; \, m$ be integers. Prove that if $2a + 3b \geq 12m + 1$, then $a \geq 3m + 1$ or $b \geq 2m + 1$.   My Attempt: I don't conceive apace how to contrive, from the one inequality in the antecedent, the two inequalities in the consequent. So a proof by contraposition may be more facile. The contrapositive is: $\text{If }  \color{Green}{a &lt; 3m + 1} \; \&amp; \; \color{#0073CF}{b &lt; 2m + 1}, \text{ then } 2a + 3b &lt; 12m + 1 \tag{*}.$  From $(*)$, $\color{Green}{2a} + \color{#0073CF}{3b} &lt; \color{Green}{6m + 2} \; + \;\color{#0073CF}{6m + 3} = 12m +5$. But this doesn't prove $(*)$.     Given Solution:  Assume that $a &lt; 3m+1$ and $b &lt; 2m+1.$ Since a and b are integers, $a ≤ 3m$ and $b ≤ 2m.$ Therefore, $2a + 3b ≤ 2(3m) + 3(2m) = 12m &lt; 12m+ 1,$ as desired. $\blacksquare$   What went wrong in my attempt? I understand the given solution but I persisted with the more natural and direct green and blue, instead of deviating to weak inequalities. Shouldn't both solutions work?  Source: Problem 4.19 on P102 (related to P90, Result 4.8) of Mathematical Proofs, 2nd ed by Chartrand et al.    $\large{\text{Supplement to Cameron Buie and pritam's Answers :}}$  What overriding, catholic lessons can be extrapolated from this example to generalise about inequalities?   Moreover, in order to circumvent the problem here (ie the loss of information from the weaker inequalities), should I always start with the strictest inequality? If so, should I always rework any weak inequality into the equivalent strict inequality?   For example, define $r \in \mathbb{R} $ and $n \in \mathbb{Z}$ and $g(...) \neq h(...)$. Then $ f(r) &lt; h(r) \require{enclose}      \enclose{updiagonalstrike}{\iff} f(r) \leq g(r).$ But $ f(n) &lt; h(n) \text{ MAY OR MAY NOT }\iff f(n) \leq g(n).$ How can I speed up data transfer between local computers on a WiFi network? I have a router with ADSL Pentagram Cerberus 6331-42. Is it normal to have transfer speeds between two computers of max 1MB/s (not 1 Mbit)? How can I set my router up to make it faster at transferring data in my local WiFi network?  I have a PC and a laptop. Both are running Windows 7. I don't use a firewall. I've set the network area up correctly; I can see other computers.  Is it possible to make the router faster by changing its values? I don't use secure encryption such as WPA or WEP; only MAC filtering.  My values in Interface Setup > Wireless are:       Here are my thoughts after few years I've published this topic:    use 5Ghz bandwidth if possible  use range extender if Your router is too far  try wifi analyzer app for mobile phone to check what channel is the less used Connectedness of the Hausdorff distance. Does anyone know a proof of connectedness of the Hausdorff distance?  I mean a proof of the following:  Theorem  If $(X, \rho )$ is a connected metric space, then $(F(X), d_h )$ is also connected.  Remark:  $F(X) = \{ A \subseteq X | A \text{ is nonempty, closed and bounded } \} $, and $d_h$ stands for the Hausdorff distance. What happens to folks who get question banned, by and large? There is a steady stream of duplicates of  coming in lately. It's got me wondering. Roughly speaking, out of say 100 folks who get this ban, how many    wander away and never interact with SO again?   do the sorts of things that might lift a ban, but don't get it lifted? do the sorts of things they should, and lift the ban? post a question of their own on Meta which we close as a dupe?   Among the continue-to-interact folks, is there a difference in success rate between those who post on Meta about it (motivated, but not good rules-readers, who nonetheless get customized advice) and those who do not (better rules readers, but working to some extent blind) - which do better?  Is there a reasonable chance of recovering from a ban, assuming you care enough to try? Get the name of an object's type What is the meaning, usage and formality of the greeting "What's up"? June 13th 2017 Microsoft blocked handling HTML markup in SharePoint calculated fields - how to get the same functionality back On June 13th 2017 all SharePoint calculated columns with HTML markup stopped working.   Basically the fields now render text (regardless of setting the data type to number). The gist of the notice from Microsoft () is:     In Microsoft SharePoint lists and libraries, calculated fields that   are running in the classic UI mode can be used to display results   based on Excel-like formulas. This is a long standing capability, and   is documented in Calculate data in lists or libraries.      Some users have added HTML markup or script elements to calculated   fields. This is an undocumented use of the feature, and we will begin   blocking execution of custom markup in calculated fields in SharePoint   Online from June 13, 2017 onwards. We are also providing this as a   configurable option for on-premises in SharePoint Server 2016 and   SharePoint Server 2013 via the June 2017 and subsequent Public   Updates.   As we don't have on premise SharePoint (online), we have to find an immediate work around, given that this impacts our processes and thus, business.   Is anyone aware of third party applications that will allow for HTML, script markup (that works with SP online)? Prefix or adjective meaning "one and a half" Is there a prefix or adjective that means "one and a half", as "tri-" or "triple" is for "three"?  The exact usage I have is to describe "18" in terms of a dozen. Where I live they've started making 18-egg cartons, and the local grocer was wondering what name to give them in his computerised cash register, hoping for a single word.  Even slang, informal or invented term would do if there isn't such a term already. Cannot access to (or find out) main Settings program Factoring $x^n + y^n$ over the integers I am new to blender (yes, laugh at the obligatory doughnut) and I when I set up the camera (I use NUM 0 to access the camera and move it into position with &quot;Lock camera to view&quot;) in the viewport it shows as the first attached image, but when I render it the image is further back as shown in the second image. Is this normal behavior or am I missing something? Prove by induction that for all $n \ge 0$:  $${n \choose 0} + {n \choose 1} + ... + {n \choose n} = 2^n.$$  In the inductive step, use Pascal’s identity, which is:  $${n+1 \choose k} = {n \choose k-1} + {n \choose k}.$$  I can only prove it using the binomial theorem, not induction. I forgot my password of a TrueCrypt file I used a few years ago.  How would I go about 'cracking' it? I'm not sure if there is a way to attack it or if it can only be done by brute-force. I used it on a Mac. I still have the Mac I used it on, but of course turned that off many times since I used it.   I have a passphrase that I thought would relate to this file. Maybe I used some variant of it. But might be something completely different. I have some other words that I might have used, but would need give it another thought how I could have used those.  Is there an automated way to test variations on what I think the passphrase was to regain access to the volume? Is there any other way I might regain access? I'm using code that I found on the .  The only problem is it uses external DLL calls that don't work in mono.  I was wondering if anyone knew of a way to accomplish the same thing as that code, but will run in both Windows using .net, and Linux using mono?  Edit:  Clarifying what I'm trying to do: I'm making a .  The program sits in the system tray and when the user presses the hot-key, it will pop up all the gadgets.  So the program doesn't have focus, so typically it won't catch any keystrokes, so I'm using the low-level keyboard hook and I hook the two keys that the user defines as the hot-keys.  But I'm using a Windows DLL call for that, which doesn't work in Linux using mono.  So I'm wondering if there's a way to do the same thing, but will run in Linux using mono? Could I have a hint for testing the convergence of the following series please?  $$\sum_{n=2}^\infty\frac{1}{(\ln n)^{\ln n}}$$  Edit  The integral test does not work because $\int_1^n\frac{1}{(\ln x)^{\ln x}}dx$ has not an elementary primitive.  Thank You. For $f$ an analytic function, what is I know roughly and informally what a confidence interval is.  However, I can't seem to wrap my head around one rather important detail:  According to Wikipedia:     A confidence interval does not predict that the true value of the parameter has a particular probability of being in the confidence interval given the data actually obtained.     I've also seen similar points made in several places on this site.  A more correct definition, also from Wikipedia, is:     if confidence intervals are constructed across many separate data analyses of repeated (and possibly different) experiments, the proportion of such intervals that contain the true value of the parameter will approximately match the confidence level   Again, I've seen similar points made in several places on this site.  I don't get it.  If, under repeated experiments, the fraction of computed confidence intervals that contain the true parameter $\theta$ is $(1 - \alpha)$, then how can the probability that $\theta$ is in the confidence interval computed for the actual experiment be anything other than $(1 - \alpha)$?  I'm looking for the following in an answer:   Clarification of the distinction between the incorrect and correct definitions above. A formal, precise definition of a confidence interval that clearly shows why the first definition is wrong. A concrete example of a case where the first definition is spectacularly wrong, even if the underlying model is correct. I have two files in a directory. One has correct permissions and the other has not. Is there a way I can "copy" the set of permissions from one file to another? Output the common lines (similarities) of two text files (the opposite of diff)? Purpose of memory alignment Admittedly I don't get it. Say you have a memory with a memory word of length of 1 byte. Why can't you access a 4 byte long variable in a single memory access on an unaligned address(i.e. not divisible by 4), as it's the case with aligned addresses?