Which is greater, $300 !$ or $(300^{300})^{1/2}$?

Which is greater among $300 !$ and $(300^{300})^{1/2}$ ? The answer is $300 !$ (my textbook's answer). I do not know how to solve problems involving such large numbers.

When should I fudge dice rolls?

When I started my first D&D campaign as a DM, I accidentally rolled and confirmed a crit on a PC from a goblin. It was an instant kill as our campaign had no cleric. That time I decided to fudge …

Holiday contest! Drawing a picture of Krampus for Yule

I've volunteered to use some of my Cthulhu reputation to sponsor a Christmas/holiday contest. You all have aced previous holiday questions, so I'm going to give you a bit more of a challenge: Draw me …

How can an extremely mathematically talented young person be helped to fulfill his/her potential?

Obviously, this question is not a research level mathematics question at all. But, I've just met an extremely mathematically talented 11 years old student and I don't know how I can help him. For ...

How to stop a background process as normal user?

I have started a wget on remote machine in background using &. Suddenly it stops downloading. I want to stop its process, then start it again. But I have just normal user access. How can I stop …

How long can you say “the late so and so”?

When you refer to the deceased, you say "the late so and so." How long can you say that? Is JFK referred to as the late John F. Kennedy? How about Abraham Lincoln?

When $x$ goes to $0$ , what happens to $\sin\left(\frac{1}{x}\right)$ and $\cos\left(\frac{1}{x}\right)$?

When $x$ approaches $0$, do $\sin\frac{1}{x}$ and $\cos\frac{1}{x}$ converge or diverge? How do you show this?

Multiple equations with a large “{” in front: alignment and labelling

I'm trying to get the equation shown in the picture. But i only manage to get the following coding. Can anyone help me to label it with numbering like the picture? I tried with \begin{eqnarray} or …

How to plot contours in the faces of a cube

I'm trying to plot contours of a function f[x,y,z] on the faces of a cube as the example below, which represents the domain of this function. Is there a way to do it in Mathematica? The ...

Euclid's Algorithm (Greatest Common Divisor)

According to Donald Knuth in "The Art Of Computer Programming", the following is how to find the greatest common divisor of two positive numbers, m and n, using Euclid's Algorithm. Divide m by …

Break on NaN in JavaScript

Is there any modern browser that raises exceptions on NaN propagation (ie multiplying or adding a number to NaN), or that can be configured to do so? Silent NaN propagation is an awful and insidious …

How is major software protected?

I am a new software developer and I wish to sell my software. I recently realized that from C++ code we can not stop the user seeing parts of the code that are related to scripts or system commands. …

Capping hit points in D&D possible without seriously breaking the game?

By "cap" I mean set a maximum level of hit points a character can acquire, let's say 20 hit points. I realize D&D is intended to be heroic fantasy, and there are other RPG systems which are more …

On some accounts I use my real name on-line(G+/fb/wiki/Personal blog), others(Q&A/Gaming) I use an alias. My question is: Security and privacy wise, what can people do with my real name? What are …

How can I configure apt-get to clean automatically after every install

Is there any way do apt-get clean after apt-get install automatically, like in other distros?

surjective map of rings with same dimension

Let $A \to B$ be a surjective homomorphism between (unital) noetherian commutative rings with the same Krull dimension. Is the kernel of this map nilpotent ? Thanks to Makoto Kato and Martin ...

Intersection of two arrays in BASH

I have two arrays like this: A=(vol-175a3b54 vol-382c477b vol-8c027acf vol-93d6fed0 vol-71600106 vol-79f7970e vol-e3d6a894 vol-d9d6a8ae vol-8dbbc2fa vol-98c2bbef vol-ae7ed9e3 vol-5540e618 ...

Why is “statistically significant” not enough?

I have completed my data analysis and got "statistically significant results" which is consistent with my hypothesis. However, a student in statistics told me this is a premature conclusion. Why? Is …

Why is Santa Claus a man?

When it comes to cities and boats named after saints, it seems that "Santa" is always female and "San" is always male. e.g. Male Saints: San Diego, San Francisco, San Antonio Female …

Example of a finite non-commutative ring without a unity

Give an example of a finite, non-commutative ring, which does not have a unity. I can't think of any thing which fits this question. I was thinking $M_2(\mathbb{R})$ but it has the identity. Any …

How can a manager of technical specialists stay relevant in a field with rapid technological change?

I am a new manager, promoted from within, and spend less and less time doing hands-on work with the technology my subordinates work on. Yet technology changes rapidly in my field. (Imagine I am a web …

Store Drupal files outside of the root

My website is running on Windows and it sits on drive C:/, however I'd like to keep all my files on drive D:/. How can I do it? I know that I can move the whole site to drive D:/ but I was wondering …

Why doesn't Java String have static string manipulation methods?

This is a programming question with a conceptual twist. I'd have posted in StackOverflow but I found similarly worded why-questions closed as not constructive. I think Programmers.SE is a better fit, …

What should I do to protect data when going across the US border with a computer?

When I successfully (legally) immigrate into the USA, I had to move some of my computers which contain a client's sensitive data/project. I was surprised when I found an article that says the CBP ...

Who was the first female dwarf identified by name in the Hobbit/LOTR saga?

While the fathers of several "son of" dwarves are named in the epic, I can't recall that a female dwarf was ever referenced by name. Who was the first female dwarf identified by name in the ...

How to convert this answer into $\ln$ form?

I find the integral Integrate[Sqrt[2 x - x^2] + x^3 Log[(9 - x^2)/(9 + x^2)], {x, 0, 2}] and got 1/2 (-36 + \[Pi] + 65 ArcTanh[4/9]) How can I write this answer has the form \$\dfrac{65}{4} \ln …

A basic question about raw pdf file output by pdftex

Consider the following simple tex file, to be compiled with pdflatex. \pdfcompresslevel=0 \documentclass{standalone} \begin{document} \hrulefill \end{document} Thanks to \pdfcompresslevel=0, the …

Correct use of Flyback or Snubber diode across Motor or Transistor?

From seeing a few schematics where the flyback or snubber diode has been placed across the transistor C-E terminals (Right Configuration), instead of what I typically seen as the the flyback being ...