Fun Facts are designed for, and work best in, lower-division college courses where the typical student is not a math student. The...
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These fun facts are at the advanced level.
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,...
Continue reading...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...
Continue reading...Irrationality by Infinite Descent
The traditional proof that the square root of 2 is irrational (attributed to Pythagoras) depends on understanding facts about the...
Continue reading...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...
Continue reading...Computability of Real Numbers
We can write a computer program that will successively print out the digits of the decimal expansion of Pi. We...
Continue reading...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 =...
Continue reading...Rationals Dense but Sparse
Well we all know that between any two real numbers there is a rational. Mathematicians like to say that the...
Continue reading...Ordinal Numbers
One of the most useful properties of the whole numbers is that every non-empty subset has a least element; this...
Continue reading...Risk-Free Betting on Different Beliefs
Alice believes that the 49ers will win the Super Bowl with probability 5/8. Bob believes that Ravens will win the...
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