I would like to create an array of number equally spaced (0.1) between 0.1 and 100  step=0.1 range_a=numpy.arange(step,100+step,step)   why my first element is   range_a[0] Out[27]: 0.10000000000000001   and not 0.1?  and how do I get an array equal to [0.1, 0.2, 0.3, ..., 100]
Consider the following code:   0.1 + 0.2 == 0.3  -&gt;  false   0.1 + 0.2         -&gt;  0.30000000000000004   Why do these inaccuracies happen?
For every vector space $V$ does there exist a linear functional $f$ ( a linear map from $V$ to $F$ the underlying field ) such that for some $ \vec v \in V$ , $f(\vec v) \ne 0$ ? If it does exist , can we prove the existence without the "axiom of choice " ? Is the existence equivalent to axiom of choice ? Using dconf-editor I tried enabling   org -&gt; gnome -&gt; nautilus -&gt; list-view -&gt; use-tree-view     but even after the check box is selected, plus a reboot, it still doesn't switch to the tree view on the side bar.  In previous versions of Nautilus / Ubuntu the side-pane-view setting used to be in the window-state section (which is now missing)    I'm I missing something, or is there no way to enable Tree View on the side bar in 14.04?  Is there a way to manually create the missing entry back in window-state ? Geometric series for two-point function In deriving the expression for the exact propagator  $$G_c^{(2)}(x_1,x_2)=[p^2-m^2+\Pi(p)]^{-1}$$   for $\phi^4$ theory all books that i know use the following argument:  $$G_c^{(2)}(x_1,x_2)=G_0^{(2)}+G_0^{(2)}\Pi G_0^{(2)}+G_0^{(2)}\Pi G_0^{(2)}\Pi G_0^{(2)}+...$$  wich is a geometric series so the formula for the exact propagator.Here  $$G_0^{(2)}$$   is the free propagator and   $$\Pi=X+Y+Z+...+W$$  is the sum of all irreducible diagrams.Here the irreducible diagrams is represented by $X,Y,Z,...,W$.  Using the path integral i can see, that  connected diagrams $D$ can be written in the form  $$D=G_0^{(2)}XG_0^{(2)}Z...G_0^{(2)}W$$  Question: But how to prove that there is no constant $C$ so that instead we have  $$D=G_0^{(2)}XG_0^{(2)}Z...G_0^{(2)}W$$  we would have  $$D=CG_0^{(2)}XG_0^{(2)}Z...G_0^{(2)}W~?$$  In the last case we would not have a geometrical serie. Can someone explain me i t please  or give me another way to derive it. I am using a premium legit version of Minecraft that I purchased. I can log into minecraft.net as well as mojang.com but I am unable to login to Minecraft the game through the minecraft.exe or the Technic launcher. The Minecraft servers are up and running fine. My internet connection is also fine. I double checked my credentials and even tried changing my password. I tried using both my username and my email. I tried all of this on two separate accounts that I own. I tried deleting my login, launcher, launcher.pack.lzma, and launcher_profiles.json and then reopening Minecraft. I tried re-downloading minecraft.exe.   Nothing has worked and I seem to have run out of options. I sent a help request to Mojang but in the meantime I was hoping that maybe you guys could offer some advice. Strange Pop-up appldnld.apple.com:80 I received a strange Pop Up message. The unsettling part is password will be sent in clear text.  Is my phone affected with any malware or app virus ? Who are the 3 men who would have a chance against Jaime Lannister in a sword fight? In Game of Thrones season 2, episode 8, "The Prince of Winterfell" , Jaime Lannister says to Brienne:     There are three men in the kingdoms who might have a chance against me [in a sword fight]   Who are those three people?                                  I don't believe this quote, or any variation, appears in the books. There was this quote from A Storm of Swords when he is fighting Brienne:     She is stronger than I am.      The realization chilled him. Robert had been stronger than him, to be sure. The White Bull Gerold Hightower as well, in his heyday, and Ser Arthur Dayne. Amongst the living, Greatjon Umber was stronger, Strongboar of Crakehall most likely, both Cleganes for a certainty. The Mountain’s strength was like nothing human. It did not matter. With speed and skill, Jaime could beat them all.   So in the books it suggest that Jaime can beat anyone, though he is only referring to people of great strength, not necessarily of great skill (somebody such as Barristan Selmy, who is not considered to be exceptionally strong but is exceptionally skillful, may be able to beat him).  Is there any canon evidence to suggest who these three people may be?  I won't accept any purely speculative answers. However if there is no direct canon quote answering the question (which I believe to be the case) I will consider answers that are strongly inferred from canonical sources (such as a canon quote saying X is the greatest fighter in the kingdom, for example). [Firmware Bug]: TSC_DEADLINE disabled due to Errata - what should I do about this? I saw several bugs and error messages when I was looking by chance into the tool called "logs".  Being a newbie in Ubuntu I have no idea how to deal with these bugs, where to report them or how to fix them.  Any help to guide me here?  The bug I have (which is listed under important) reads:  [Firmware Bug]: TSC_DEADLINE disabled due to Errata; please update microcode to version: 0x52 (or later) Today I found something strange on my newly installed Windows 7 OS - my "users" folder C:\Users was shared and "Everyone" had full access... I disabled that and now it seems fine, however I'm a bit scared actually, I'd like to know what caused that and if my system is compromised. Deriving even odd function expressions What is the logic/thinking process behind deriving an expression for even and odd functions in terms of $f(x)$ and $f(-x)$?  I've been pondering about it for a few hours now, and I'm still not sure how one proceeds from the properties of even and odd functions to derive: $$\begin{align*} E(x) &amp;= \frac{f(x) + f(-x)}{2}\\ O(x) &amp;= \frac{f(x) - f(-x)}{2} \end{align*}$$ What is the logic and thought process from using the respective even and odd properties, $$\begin{align*} f(-x) &amp;= f(x)\\    f(-x) &amp;= -f(x) \end{align*}$$   to derive $E(x)$ and $O(x)$?    The best I get to is: For even: $f(x)-f(-x)=0$ and for odd: $f(x)+f(-x)=0$  Given the definition of $E(x)$ and $O(x)$, it makes a lot of sense (hindsight usually is) but starting from just the properties. Wow, I feel I'm missing something crucial. Compare the statistical significance of the difference between two polynomial regressions in R So first of all I did some research on this forum, and I know   questions have been asked but they usually haven't been answered properly or sometimes the answer are simply not detailed enough for me to understand. So this time my question is : I have two sets of data, on each, I do a polynomial regression like so :  Ratio&lt;-(mydata2[,c(2)]) Time_in_days&lt;-(mydata2[,c(1)]) fit3IRC &lt;- lm( Ratio~(poly(Time_in_days,2)) )   The polynomial regressions plots are:    The coefficients are :  &gt; as.vector(coef(fit3CN)) [1] -0.9751726 -4.0876782  0.6860041 &gt; as.vector(coef(fit3IRC)) [1] -1.1446297 -5.4449486  0.5883757    And now I want to know, if there is a way to use an R function to do a test that would tell me whether or not there is a statistical significance in the difference between the two polynomials regression knowing that the relevant interval of days is [1,100].  From what I understood I can not apply directly the anova test because the values come from two different sets of data nor the AIC, which is used to compare model/true data.  I tried to follow the instructions given by @Roland in the related question but I probably misunderstood something when looking at my results :  Here is what I did :   I combined both my datasets into one.  f is the variable factor that @Roland talked about. I put 1s for the first set and 0s for the other one.  y&lt;-(mydata2[,c(2)]) x&lt;-(mydata2[,c(1)]) f&lt;-(mydata2[,c(3)])  plot(x,y, xlim=c(1,nrow(mydata2)),type='p')  fit3ANOVA &lt;- lm( y~(poly(x,2)) )  fit3ANOVACN &lt;- lm( y~f*(poly(x,2)) )   My data looks like this now :    The red one is fit3ANOVA which is still working but I have a problem with the blue one fit3ANOVACN the model has weird results. I don't know if the fit model is correct, I do not understand what @Roland meant exactly.  Considering @DeltaIV solution I suppose that in that case :  The models are significantly different even though they overlap. Am I right to assume so ? Are there areas of mathematics (current or future) that cannot be formalized in set theory? I often read that ZFC can formalize "most" of everyday mathematics, but I could never find an example which it cannot. The closest I got is differential geometry (DF), where some article mentions that the translation from concepts of DF into set theory would render it almost "meaningless", in the sense that any intuitions one could have would be lost in the translation. So, if I didn't misunderstand, at least in theory, the translation could be done, so that a future AI machine could prove theorems of differential geometry using set theory. On the other hand, the Stanford Encyclopedia of  Philosophy states that "all of mathematics can be reduced to a formal system of set theory"().   So, the questions are:    Is there any current area of mathematics that could be not formalized within set theory? If so, which ones? and  Is there any reason to think that every math of the future will be always formalizable in set theory? any references to read on the subject are welcomed!   Clarification: by set theory I am not restricting to ZFC, but to any flavor of it, including all additional axioms you want (about large cardinals or any kind) Removing elements with Array.map in JavaScript I would like to filter an array of items by using the map() function. Here is a code snippet:  var filteredItems = items.map(function(item) {     if( ...some condition... )     {         return item;     } });   The problem is that filtered out items still uses space in the array and I would like to completely wipe them out.  Any idea?  EDIT: Thanks, I forgot about filter(), what I wanted is actually a filter() then a map().  EDIT2: Thanks for pointing that map() and filter() are not implemented in all browsers, although my specific code was not intended to run in a browser. Nonstandard normal distribution Showing equality of sequence of holomorphic functions to limit function if converges uniformly locally I do not know how to proof following question:  Let $D$ be a domain in $C$.  ${{f}_{n}}$ be a sequence of holomorphic functions on $D$ that converges uniformly locally to a function non-constant $f$. Show that for each $z\in D$, there is a sequence ${{z}_{n}}\to z$ as ${{f}_{n}}({{z}_{n}})=f(z)$ for all sufficiently large $n$.  Actually, I know that I should use an assumption such as: ${{f}_{n}}({{z}_{n}})\ne f(z)$  Therefore, there is compact set    that  $\left\| {{f}_{{{n}_{k}}}}({{z}_{{{n}_{k}}}})-f(z) \right\|&gt;\varepsilon $  Then I think I have to use Montel theorem, but I do not know how to show the contradiction. How do I get my Mac to boot from an Ubuntu USB key? Mysql Pivot rows into dynamic columns with unknown number of columns I have an output of a query as follows:  bid  | code | amount        | ----------------------------- 2915 | BF   |   -10700.00   | 2915 | YQ   |   -300.00     | 2915 | YR   |   0.00        | 2915 | YM   |   0.00        | 2915 | WO   |   -153.00     | 2915 | IN   |   -329.00     | 2915 | K3   |   0.00        | 2915 | CUTE |   -50.00      | -----------------------------   I need to convert the values in code column to individual columns with column name as corresponding code and amount shall be the value.  bid  | BF       | YQ     | ... | CUTE  | ---------------------------------------- 2915 | -10700.00| -300.00| ... | -50.00|   The issue is that the result of my initial query has dynamic codes and hence need to generate columns accordingly.  Already tried the following logic but couldn't achieve the goal:   , ,   All the above links use some expression or the other to generate the columns.   My original resulting rows are result of simple select on multiple joined tables, and has no calculation or expression scope.  Kindly suggest some pointer or hint on how to achieve this.  Many thanks in advance. Crash or "segmentation fault" when data is copied/scanned/read to an uninitialized pointer How to force NSLocalizedString to use a specific language I'm trying to purchase a domain name that was registered and apparently already expired. This is its status:  Status: clientHold http://www.icann.org/epp#clientHold Status: clientTransferProhibited http://www.icann.org/epp#clientTransferProhibited Status: redemptionPeriod http://www.icann.org/epp#redemptionPeriod Updated Date: 14-oct-2015 Creation Date: 01-sep-2014 Expiration Date: 01-sep-2015   From what I'm seeing from ICANN policies, it should already be available to be registered by third parties, but maybe I'm missing something. When will it become available for me to register it? Does Wasserstein distance require the source and target distributions to have the same mass? If we minimize the Wasserstein loss, $$W_1 (P_S, P_T) = \underset{\gamma \in \Pi}{\text{min }} \sum_{x,y} |x-y|\gamma(x,y)$$ which means we are looking for the coupling $\gamma(x,y)$ that minimizes the cost of moving mass from the source distribution $P_S$ to the target distribution $P_T$,  Do the masses of the source and target distributions have to be identical? If so or not, how are the masses of $P_T$ and $P_S$ accounted for mathematically in, or when minimizing, the shown formula, or what might be missing/overlooked by the Wasserstein approach overall due to the mass differences?