The “guess what number I’m thinking of” problem

This post is, to some extent, a follow-up to my post on the two envelopes problem. As before, you're the subject of an experiment. Your adversaries, who I'll call "Team E", present you with two envelopes, each containing a slip of paper with a different number written on it. The numbers could be any (Real) … Continue reading The “guess what number I’m thinking of” problem

Yes, pi is wrong. Sorry about that.

Which is the more fundamental constant: π or 2π? As pi day approaches, I think it's important for everyone to state their thoughts on this contentious matter. Here are the main options: π is more fundamental. (the establishment position)2π is more fundamental. (the progressive position)They're about equally fundamental. (the "both sides" position)Any rational multiple of … Continue reading Yes, pi is wrong. Sorry about that.

Alternative to Cantor’s diagonalization argument

How does one prove that there are more real numbers than integers? There are an infinite number of each, but the infinity of the real numbers is, in a strict sense, larger than the infinity of the integers. In math terminology, the set of reals has a larger cardinality. Roughly speaking, it's equivalent to saying … Continue reading Alternative to Cantor’s diagonalization argument

The new record largest known prime number

A few days ago, the discovery of a new record largest known prime number (282,589,933−1) was announced, making my post on "finding" record prime numbers somewhat obsolete. I could update it, but that would be silly. Instead, I'll discuss these record primes. It happens every couple of years: A new record large prime number is … Continue reading The new record largest known prime number