## 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}} …