Cardinality of the set of continuous functions
Cardinality of set of real continuous functions
How do I create an Excel (.XLS and .XLSX) file in C# without installing Microsoft Office? How can I create an Excel spreadsheet with C# without requiring Excel to be installed on the machine that's running the code? Can I travel to Australia in less than 2 weeks if I transfer my visa to my new passport? I transferred my visa to my new passport and it’s saying it takes 2 weeks to come, my flight is Sunday I arrive in Sydney Monday at night, I still have my old passport! If I bring that will they let me go into the country because my new one literally arrived two days ago! And the visa will be transferred in 2 weeks! Will I have to push my flight or will I be left? Reducibility of polynomials modulo p How do I upload a file to an SFTP server in C# (.NET)? Does a free .NET library exist with which I can upload a file to a SFTP (SSH FTP) server, which throws exceptions on problems with the upload and allows the monitoring of its progress? If $F\supset E$ and $E\supset k$ are normal extensions. I want a counter-example where $F\supset k$ is not normal How to enable linking floating point library in TurboC? Python - Convert string representation of date to ISO 8601 How can one request reconsideration of a   after a certain period of time, let us say after one year? Why is ANOVA taught / used as if it is a different research methodology compared to linear regression? ANOVA is equivalent to linear regression with the use of suitable dummy variables. The conclusions remain the same irrespective of whether you use ANOVA or linear regression.   In light of their equivalence, is there any reason why ANOVA is used instead of linear regression?   Note: I am particularly interested in hearing about technical reasons for the use of ANOVA instead of linear regression.   Edit  Here is one example using one-way ANOVA. Suppose, you want to know if the average height of male and females is the same. To test for your hypothesis you would collect data from a random   sample of male and females (say 30 each) and perform the ANOVA analysis (i.e., sum of squares for gender and error) to decide whether an effect exists.  You could also use linear regression to test for this as follows:  Define:  $\text{Gender} = 1$ if respondent is a male and $0$ otherwise. $$ \text{Height} = \text{Intercept} + \beta * \text{Gender} + \text{error} $$ where: $\text{error}\sim\mathcal N(0,\sigma^2)$  Then a test of whether $\beta = 0$ is a an equivalent test for your hypothesis. How do I post text so that it is formatted as code?  What do I need to do so that my code shows up properly &mdash; not escaped or removed &mdash; when posted? And how to get the correct syntax highlighting?     For more information, see "" in the . Story about space explorers who communicate but then decide they must destroy each other I'm looking for a sci-fi story or novel from many years ago where a deep space explorer encounters an alien explorer. The explorers learn to communicate; but on parting, each decides to destroy the other in order to protect his own world. What is known about $\mathcal C^\infty$ functions $\mathbb R\to\mathbb R$ that always take rationals to rationals? Are they all quotients of polynomials? If not, are there any that are bounded yet don't tend to a limit for $x\to +\infty$? If there are, then can we also require them to be analytic?  (This is basically just a random musing after I found myself using trigonometric functions twice in unrelated throwaway counterexamples. It struck me that it was kind of conceptual overkill to whip out a transcendental function for the purpose I needed: basically that it had to keep wiggling forever. I couldn't think of a nice non-trancendental function to do this job, however, and now wonder whether that is because they can't exist). Is the function Riemann integrable? If yes, obtain the value of $\int_0^1f(x) \ dx$      $f(x) = \begin{cases} \frac {1}{n},  &amp; \frac{1}{n+1}&lt;x\le\frac{1}{n}\\ 0, &amp; x=0 \end{cases}$   My attempt  $f$ is bounded and monotonically increasing on $[0,1]$. Also, $f$ has infinite discontinuities but only one limit point. Therefore $f$ is Riemann integrable. Now, to calculate the integration  $\int_0^1f(x) \ dx=\int_{1/2}^{1}1 \ dx + \int_{1/3}^{1/2}\frac{1}{2} \ dx + \int_{1/4}^{1/3}\frac{1}{3} \ dx+...$  $=\sum_{n=1}^\infty \frac{1}{n^2}-\frac{1}{n}+\frac{1}{n+1}$  How do I proceed from here? How do I calculate these summations? I know $\sum \frac{1}{n}$ is $\log 2$, but not the other two summations. Set a polygon's normal's orientation as the objects local rotation orientation (if every polygon is an object) Let $f$ be continuous on $ [a,b]$, differentiable on $ (a,b) $ and $ f(x) \neq 0 \forall x \in (a,b) $ Prove $ \exists c \in (a,b) $ such that Why do we need sigma-algebras to define probability spaces? Why are Alkaline, NiMH, and Li-ion AA measured differently (mAh, mWh, etc)? Looking around Amazon, it seems that different types of batteries are measured differently:  Does anyone know why?   Li-ion are measured in mWh    (Cheap-Os)  3000mWh AmpTorrent  NiMH are measured in mAh      Alkalines are typically not measured   "Long Lasting" Duracell "Longest Lasting" Energizer    I assume that Alkalines are not measured for some sort of historical reason with marketing departments?  ... or is it that alkalines so mystical and unreliable that giving them a measurement is too aggressive? Or that switching to non-toxic / non-mercury was such a bad move in performance that measurements had to be removed in the 90s so people wouldn't know?  Perhaps NiMH are measured in mAh because the voltage can very so greatly and mWh doesn't make sense?  Are Li-ion measured in mWh because that's more consistent with non-battery measurements and they do deliver reliable voltage? getting Checkpoint VPN SSL Network Extender working in the command line The official Checkpoint out command line tool from CheckPoint, for setting up a SSL Network Extender VPN is not longer working from the Linux command line. It is also no longer actively supported by CheckPoint.  However, there is a promising  project, that tries to replicate the Java applet for authentication, that talks with the snx command line utility, called snxconnect.   I was trying to put snxconnect text utility to work in Debian Buster, doing:  sudo pip install snxvpn   and  export PYTHONHTTPSVERIFY=0 snxconnect -H checkpoint.hostname -U USER    However, it was mostly dying either with an HTTP error of:   HTTP/1.1 301 Moved Permanently:   or:  Got HTTP response: HTTP/1.1 302 Found   or:  Unexpected response, try again.   What to do about it?  PS. The EndPoint Security VPN official client is working well both in a Mac High Sierra and Windows 10 Pro. Account not acting as an administrator correctly My account, david, is in the Administrators group on a Windows 7 machine.  I am still having problems with programs that I should be able to use, such as SQL Server. Specifically, my account seems to not have correct permissions when I am working.  I know with an Administrator account I should have full access. How can I force my account (david) to act like an admin account and have full access to everything? Gaussian Integers and Quotient Rings Show that $\mathbb{Z}[i]/(2+3i)$ is a finite field.    By applying some isomorphisms and realizing $\mathbb{Z}[i]$ as the quotient ring of $\mathbb{Z}[x]/(x^{2}+1)$, I found that:  $\mathbb{Z}[i]/(2+3i) \cong \mathbb{Z}[x]/(x^2+1,2+3x)$  However, I run into trouble as I can't divide $x^{2}+1$ by $2+3x$ in $\mathbb{Z}[x]$. What would be another way to approach the problem?  Thanks for the help.