Prove if $n^2$ is even, then $n$ is even.
I am just learning maths, and would like someone to verify my proof. Suppose $n$ is an integer, and that $n^2$ is even. If we add $n$ to $n^2$, we have $n^2 + n = n(n+1)$, and it follows that ...
Square root of $8^3$
I'm only in intermediate algebra. I know that $\sqrt{8^3}$ is equal to $16\sqrt{2}$ but could you simply explain the process on how to get to that?
The importance of interfaces in Java
Let's say we have two classes, Tiger and Aeroplane. One thing in common for these two types is the Speed. I know that it would be illogical to create a superclass ClassWithSpeed and then derive ...
What is the benefit of a Cisco “top of rack” design?
Aside from the obvious cabling mess you avoid (which I know for us as network engineers is great, but hard to use as an excuse when reasoning with someone who sees no point in it), what do you gain …
Are there other places with gardens like those at Versailles?
The Gardens of Versailles are world famous, and apparently receive over 6 million visitors a year. They're stunning gardens to visit, but I can't help but think that some other European courts might …
How to create a file which is named like a command line argument?
I was wondering how to make a file named as a flag, e.g., if I wanted to make a folder named -a, what commands would do the trick? I tried mkdir '-a', mkdir \-a, and neither worked. I'm on Ubuntu.
Why is “for all $x\in\varnothing$, $P(x)$” true, but “there exists $x\in\varnothing$ such that $P(x)$” false?
There exists an $X\in A$ such that $P(X)$. When $A$ is the empty set then this statement is false because there is nothing in $A$ that when plugged in for $X$, makes $P(X)$ come out True. However, …
Etymology of “flounder”
Online Etymology Dictionary reads: flounder (v.) 1590s, perhaps an alteration of founder (q.v.), influenced by Dutch flodderen "to flop about," or native verbs in fl- expressing clumsy motion. …
Adjusting command behavior based on argument type
I have a following command in my latex document: \newcommand{\ApplyGradient}[1]{ \pgfmathsetmacro{\PercentColor}{100.0*(#1+0.2)/1.3} \textcolor{black!\PercentColor}{#1}} …
How do I stop bash from syntax checking sourced files?
I have the following code in a file that is sourced by both zsh and bash. if test $SHELLNAME = zsh ; then lss() { l -l ${1:-.}/*(s,S,t); } laf() { l ${1:-.}/.*(.); } lad() { l -d ...
Best practice for dual-homing site with two ISPs?
I am subscribed to two ISPs, a fast expensive one and a cheap but slower one. They use different technologies, cable and ADSL, so there isn't much of a single point of failure, and all my comms ...
Doubt in $\varepsilon$-$\delta$ proof of continuity of $x^2$
I have one elementary doubt on the proof that $f(x)=x^2$ is continuous for every $a \in \Bbb R$. The initial steps usually presented are: to deduce which $\delta$ will work we write: ...
Is the Greenbound Summoning Feat as powerful as it looks, or am I missing something?
Druids have a feat called Greenbound Summoning (Lost Empires of Faerun, p. 8), which has the following benefit: "All animals that you summon using summon nature's ally acquire the greenbound template …
Solving summation $2n+2^2(n-1)+2^3(n-2)+…+2^n$
Can anyone help me with this summation? I tried to use the geometric series on this, but I can't use that. $$2n+2^2(n-1)+2^3(n-2)+....+2^n$$ I am trying to do this for studying algorithms. Can we get …
How do I draw a Circular Graph colored like this in Mathematica?
I must plot some data in radians and would like to use this image as a background to that graph. Although it looks good the lines are degraded in image form. thus the reason for this question. Can …
Differentiate $g(t)= {e^t - e^{-t} \over e^t + e^{-t}}$
I'm having some trouble trying to differentiate the function $g(t)= \dfrac{e^t - e^{-t}}{e^t + e^{-t}}$ Can someone help me? Thanks a lot!
Routing via Cisco ASA is changing TCP sequence/ACK numbers
Our network has a dedicated VPN appliance that sits inside the office network. We have a Cisco ASA with a static route that routes the VPN subnets to the VPN appliance. So a typical request from the …
Why arrow keys are not recommended in Vim
"Never use arrow keys in Vim!" I heard this from a random speaker, but didn't have the chance to ask him why. Also, if you don't use the arrow keys, how can you move the cursor in the Insert ...
Is the following polynomial reducible over Q?
I am looking at an exercise saying that "Demonstrate that x4-22x2+1 is reducible over Q. I have the solution manual and it solves like the following: If x4-22x2+1 is reducible over Z, then it factors …
Should I make a package or class for my usual preamble, or include it in every document?
This TeX.SE thread is a good resource for how to make your usual preamble into a package or document class. I would like to know why I should do that. What are the pros and cons of doing so, as ...
To which group is the $\mathbb Z_{20}^*$ isomorphic?
I have a question saying that to which group is $\mathbb{Z}_{20}^{*}$ is isomorphic, where $\mathbb{Z}_{20}^{*}$ is the set of the not zero divisors of $\mathbb{Z}_{20}$. Here is what i think: ...
Why is there no apparent relation between focal length and physical lens size
For example the Nikkor 20mm lens has a phsyical length of 42.5mm! That's more than twice the focal length! And if you consider the sensor is not directly on the surface of the lens mount, the ...
Completely unable to use the Steam client
I am on 64-bit Windows 7 Professional. I am unable to use the Steam client at all. The problem began when I loaded Steam today and went to my Library tab--it caused the client to crash. I do not have …
Is There A Function Of Constant Area?
If I take a point $(x,y)$ and multiply the coordinates $x\times y$ to find the area $(A)$ defined by the rectangle formed with the axes, then is there a function $f(x)$ so that $xy = A$, regardless of …
Prove $\sin \left(1/n\right)$ tends to $0$ as $n$ tends to infinity.
I'm sure there is an easy solution to this but my mind has gone blank! Any help on proving that $\sin( \frac{1}{n})\longrightarrow0$ as $n\longrightarrow\infty$ would be much appreciated. This ...
In languages that don't allow underscores in integer constants, is it a good practice to create a constant for 1 billion?
In languages that don't allow underscores in integer literals, is it a good idea to create a constant for 1 billion? e.g. in C++: size_t ONE_BILLION = 1000000000; Certainly, we shouldn't create …
Show that $n \ge \sqrt{n+1}+\sqrt{n}$
(how) Can I show that: $n \ge \sqrt{n+1}+\sqrt{n}$ ? It should be true for all $n \ge 5$. Tried it via induction: $n=5$: $5 \ge \sqrt{5} + \sqrt{6} $ is true. $n\implies n+1$: I need to show ...
10V from USB port
I want to connect a loading cell to the computer via USB port. The recommended excitation voltage of the load cell is 10V, and USB output is 5V. The current through the load cell is about 20mA at ...
Symbol for “if and only if”: $\implies$ or $\iff$?
I was wondering about the iff sign in maths. I've never learned about it in school & see it a lot online. Usually the sign looks like this: $\implies$, but in math.stackexchange I always see this: …
Why does the email subject appear before the body when composing an email?
Note: I am not talking about reading experience, I am focusing on the experience of composing email. I am very aware of this issue since it happens to me all the time, and I am pretty sure that it …
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