Is there an argument, apart from experiments, that we know this is true?   And if we only know it by experiment, how do we know the experiments are precise enough to conclude this?  Stated differently, what argument is there that prevents us from replacing c in the Lorenz transformations by $c' = c + \epsilon$
I will try to be as explanatory as possible with my question. Please also note that I have done my share of googling and I am looking for simple language preferable with some example so that I can get some insight in this subject.  My question is what is so special about $c$? Why only $c$. Its like chicken and egg puzzle for me. Does Einstein reached to $c$ observing light or does he got to light using some number which turned out equal to $c$.   Why is $c$ not relative. If something has zero rest mass like a photon why they only travel at $c$ in vacuum and not with $c+1$ or $c-1$?
Let $L$ be a linear operator on a complex vector space $V$, how to show that eigenvalues of $L^\dagger L$ are positive? I guess this might be a statement taught in a functional analysis class or an advanced linear algebra class? Does time stretch all the way back for infinity or was there a point when time appears to start in the universe?  I remember reading long ago somewhere that according to one theory time began shortly before the creation of the universe.  Does time have a starting point of note? Codomain of function complete implies function space complete Let $(X,d_X)$ and $(Y,d_Y)$ be two metric spaces.   Let $(C_b(X,Y), d_C)$ be a function space with the metric $$d_C(f,g):=\sup\limits_{x\in X} d_Y(f(x), g(x)).$$  Prove that if $(Y,d_Y)$ is complete then $(C_b(X,Y), d_C)$ is complete.  Unfortunately, I have no idea how to approach this problem. I can think of something like this:  Let $(y_k)_k\subset Y$ be a Cauchy sequence converging to $y\in Y$. Then there exists some $f\in C_b(X,Y)$ such that $f(x_k)=y_k$ for all $k\in \mathbb N$. Since $f$ is continuous, $\lim\limits_{k\to\infty} d_Y(f(x_k), y)=0$.  But how do I go from here? As far as I understand, what needs to be proved is that any Cauchy sequence of functions in $C_b(X,Y)$ converges in $C_b(X,Y)$, that is, that the limit is bounded and continuous. But how do we devise such a sequence of functions? ParametricPlot3D and Sphere Graphics How to verify iOS app integrity? If I write an app for iOS and it's accepted by the AppStore, how do I know if the app is actually the app I compiled and has not being substituted/altered by, say, a "Man in the middle" style interception/attack? Is there a way to do a checksum either after the fact or from inside the app itself? Finding the id of a parent div using Jquery Trigonometric Uncertainty Propagation At work we are being asked to create XML files to pass data to another offline application that will then create a second XML file to pass back in order to update some of our data. During the process we have been discussing with the team of the other application about the structure of the XML file.   The sample I came up with is essentially something like:  &lt;INVENTORY&gt;    &lt;ITEM serialNumber="something" location="something" barcode="something"&gt;       &lt;TYPE modelNumber="something" vendor="something"/&gt;     &lt;/ITEM&gt; &lt;/INVENTORY&gt;   The other team said that this was not industry standard and that attributes should only be used for meta data. They suggested:  &lt;INVENTORY&gt;    &lt;ITEM&gt;       &lt;SERIALNUMBER&gt;something&lt;/SERIALNUMBER&gt;       &lt;LOCATION&gt;something&lt;/LOCATION&gt;       &lt;BARCODE&gt;something&lt;/BARCODE&gt;       &lt;TYPE&gt;          &lt;MODELNUMBER&gt;something&lt;/MODELNUMBER&gt;          &lt;VENDOR&gt;something&lt;/VENDOR&gt;       &lt;/TYPE&gt;    &lt;/ITEM&gt; &lt;/INVENTORY&gt;   The reason I suggested the first is that the size of the file created is much smaller. There will be roughly 80000 items that will be in the file during transfer. Their suggestion in reality turns out to be three times larger than the one I suggested. I searched for the mysterious "Industry Standard" that was mentioned, but the closest I could find was that XML attributes should only be used for meta data, but said the debate was about what was actually meta data.  After the long winded explanation (sorry) how do you determine what is meta data, and when designing the structure of an XML document how should you decide when to use an attribute or an element? Counting surjective functions How did Toru and Koji pass the entrance exam in My Hero Academia? I have seen some comments and speculations about the robot having an off switch or whatever. But I want to know if there is any source material or comment from the author on how they managed to pass the exam.  I have only seen the actual author's comment on Mineta:     But I was wondering if there are author notes for the other characters. Indentation shortcuts in Visual Studio If $(a,b)=1$ then prove $(a+b, ab)=1$. How do I perform an IF...THEN in an SQL SELECT statement?  For example:  SELECT IF(Obsolete = 'N' OR InStock = 'Y' ? 1 : 0) AS Saleable, * FROM Product References for multivariable calculus Due to my ignorance, I find that most of the references for mathematical analysis (real analysis or advanced calculus) I have read do not talk much about the "multivariate calculus". After dealing with the single variable calculus theoretically, it usually directly goes to the topic of measure theory.    After reading the wiki article "", I'd like to find the rigorous proof for this test. The first book comes to my mind is Courant's Introduction to Calculus and Analysis which includes the multivariate case in the second volume.   Motivated by this, I'd like to put the question here:     What are the usual references for the   theoretical treatment for   ? Can binary data be ordinal? Binary data is often mentioned as a nominal sub-category, especially in such examples as female/male, smoker/non-smoker, etc. However, binary data with such values as pass/fail, correct/incorrect, absent/present, etc, seems to give some weight to its values. It's not like in the example of the gender, where both values are equal and differ primarily by the nominal and other context-related traits. Instead, this type of binary data clearly indicates that one value means something and the other means nothing.   In case of such distinction, can binary be considered ordinal? If yes, what are statistical tests that are usually used for such data? Also, are there any interesting books or papers on this case? In many machine learning applications, the so called data augmentation methods have allowed building better models. For example, assume a training set of $100$ images of cats and dogs. By rotating, mirroring, adjusting contrast, etc. it is possible to generate additional images from the original ones.  In the case of images, the data augmentation is relatively straightforward. However, suppose (for example) that one has a training set of $100$ samples and few hundred continuous variables that represent different things. The data augmentation does not anymore seem so intuitive. What could be done in such case? Interpretation of ROC curve Add days to JavaScript Date Rough Smart objects problem in Photoshop I am using Adobe CC(2015) latest version and the behaviour of the smart objects isn't normal. When I paste a vector from Illustrator to Photoshop, the vector looks low quality or rough.   ORIGINAL  IN PHOTOSHOP   However, if I click over the smart object layer(in Photoshop)and this is opened in Illustrator, the vectors looks as the original one.   VECTOR OPENED IN ILLUSTRATOR FROM PHOTOSHOP SMART OBJECT   How can I solve this? What is the fastest way to convert float to int on x86 What is the fastest way you know to convert a floating-point number to an int on an x86 CPU.  Preferrably in C or assembly (that can be in-lined in C) for any combination of the following:   32/64/80-bit float -> 32/64-bit integer   I'm looking for some technique that is faster than to just let the compiler do it.