Let’s take a moment to get our hands on some sets of numbers and the arithmetic progressions those sets contain, starting with the prime numbers, perennial favorites of math enthusiasts.

The mapping works out exactly. Neither natural nor even numbers remain at the end. Therefore, both sets contain the same number of elements.

In 1886 the mathematician Leopold Kronecker famously said, “God Himself made the whole numbers — everything else is the work of men.” Indeed, mathematicians have introduced new sets of numbers besides ...

The set of odd numbers is therefore sum-free. In a 1965 paper, the prolific mathematician Paul Erdős asked a simple question about how common sum-free sets are.