## Top new questions this week:

### Does the string of prime numbers contain all natural numbers?

Does the string of prime numbers $$2357111317\ldots$$ contain every natural number as its sub-string?

(elementary-number-theory) (prime-numbers)

### Self-learning mathematics - help needed!

First, I apologise for the nebulous nature of my title but I can't adequately explain myself concisely. I am about to start an MSc in pure maths after a fairly shaky undergraduate degree. I am very …

(self-learning) (learning)

### When does L' Hopital's rule fail?

This thought jumped out of me during my calculus teaching seminar. It is well known that the classical L'Hospital rule claims that for the $\frac{0}{0}$ indeterminate case, we have:  …

(calculus) (teaching)

### how to get $f(x)$ if we know $f(f(x))=x^2+x$

how to get $f(x)$ if we know $f(f(x))=x^2+x$ Is there elementary function of $f(x)$ satisfy the equation?

(functions) (functional-equations)

### Math symbol in German thesis from 1963

I have the following math symbol in a German thesis written in 1963. Is it anything more than just a function name? It is used in the following context and then goes on to state that "If the …

(notation) (math-history)

### What is the motivation for quaternions?

I know imaginary numbers solve $x^2 +1=0$, but what is the motivation for quaternions?

(soft-question) (math-history) (quaternions)

### Why is an image called an "image"?

Given a function $f : A \to B$, the image, denoted by $\operatorname{Im}f$ is the set of all $f(x)$ where $x \in A$. Why do we call this set the image? When was it first used, and what motivated its …

(functions) (elementary-set-theory) (soft-question) (terminology) (math-history)

## Greatest hits from previous weeks:

### What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)

I'm a children's book writer and illustrator, and I want to to create a book for young readers that exposes the beauty of Mathematics. I recently read Paul Lockhart's essay "The Mathematician's …

(soft-question) (recreational-mathematics) (education) (big-list) (teaching)

### What is the practical difference between a differential and a derivative?

I ask because, as a first-year calculus student, I am running into the fact that I didn't quite get this down when understanding the derivative: So, a derivative is the rate of change of a function …

(calculus)

### Fractional Part of $a^n$

Prove that there exists a real number $a>1$, such that $\{a^n\}$ belongs to $[\frac{1}{3},\frac{2}{3}]$ for all positive integers $n$ and $\lfloor a^n\rfloor$ is even iff $n$ is a prime. …

(real-analysis) (contest-math)

### How many hamilton paths can a non-hamiltonian graph have?

What is the maximum number of hamilton paths a graph with $n$ vertices can have without having a hamiton cycle ? If my turbo pascal program works well, the first few values for $3,4,...$ vertices …

(graph-theory) (hamiltonian-path)