This curious property is one reason some scholars rejected the concept of infinite sets more than 100 years ago. For example, the set of even numbers E = {0, 2, 4, 6, …} is a proper subset of ...

For example, the number line is infinite, regardless of whether you start it at –∞, 0 or 1. ... In this way, Cantor also studied the cardinality of infinite sets. For example, ...

Szemerédi had been examining sets that contain a “positive fraction” of all the integers. Take, for example, the set containing all multiples of 5. As you look at bigger and bigger swaths of the ...