infinity blade

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.

Veritasium explains how jet engines run hotter than their components' melting points, using cooling air and single-crystal superalloy turbine blades. It covers how the blades are grown as aligned crystals.

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.