These fun facts are at the advanced level.

## How to Use Fun Facts

Fun Facts are designed for, and work best in, lower-division college courses where the typical student is not a math student. The...

## Liouville Numbers

Are there any real numbers that are NOT algebraic, i.e., expressible as the root of a non-zero polynomial with integer coefficients? In fact,...

## Does Order of Addition Matter?

From your earliest days of math you learned that the order in which you add two numbers doesn’t matter: 3+5...

## Irrationality by Infinite Descent

The traditional proof that the square root of 2 is irrational (attributed to Pythagoras) depends on understanding facts about the...

## Dedekind Cuts of Rational Numbers

Given a number line with equally spaced tick marks one unit apart, we know how to measure rational lengths: the...

## Computability of Real Numbers

We can write a computer program that will successively print out the digits of the decimal expansion of Pi. We...

## Fermat’s Last Theorem

There are lots of Pythagorean triples; triples of whole numbers which satisfy:x2 + y2 = z2. But are there any which satisfyxn + yn =...

## Rationals Dense but Sparse

Well we all know that between any two real numbers there is a rational. Mathematicians like to say that the...