uncountable infinity

Numberphile's James Grime explains Cantor's result that some infinities are bigger than others, including why the reals outnumber the integers. It is a short, accessible introduction to countable and uncountable infinity.

Vsauce's Michael Stevens takes viewers past infinity using transfinite numbers, ordinals and cardinals, with input from mathematician Hugh Woodin. It is a fast-paced, mind-bending tour of different sizes of infinity.

IGN's 2010 trailer for Infinity Blade, an Unreal Engine fighting game for iPhone, iPad and iPod. It shows off gameplay and the visuals of the mobile game.

Veritasium shows how Hilbert's infinite hotel can still run out of room, using infinite buses of guests. It explains the surprising answer in a short animated segment.

Vsauce's roughly 24 minute explainer on the Banach-Tarski paradox, building from infinity and set theory to the decomposition of a sphere into pieces that form two spheres.

John A. De Goes's Scalapeno keynote argues that Scala's popularity is declining because of compile times, complexity and compatibility problems. He proposes a path for Scala to survive, including a simplified functional subset.

Tom Murphy (suckerpinch) presents a deliberately trollish computer architecture built on IEEE-754 floating point, using NaN and infinity to define logic gates. He builds working hardware around the idea.

An excerpt from an RSA event in which physicist David Deutsch makes the case for optimism as a driver of progress in the 21st century. It is a short highlight of a longer discussion.

A clip from Mr. Show season 3 in which characters insist that 24 is the highest number. It is a short absurdist sketch about counting.