Cantor's Diagonal Argument
There are more numbers between 0 and 1 than there are whole numbers in all of eternity. Both lists are infinite.
189116 min read
German mathematics
Georg Cantor
1845 – 1918
Born in Saint Petersburg, professor at Halle for his entire career, and the creator of set theory. He proved that infinite sets come in different sizes, invented the transfinite cardinals and ordinals, and defended the completed infinite against fierce opposition — most bitterly from his former teacher Leopold Kronecker. He suffered recurrent depression from 1884 and died in a sanatorium in Halle.
2 entries
Hilbert's Grand Hotel
A hotel with infinitely many rooms is completely full. At two in the morning, one more guest arrives. The manager finds them a room.
1924 (lectures), 1947 (popularised)13 min read