In an April fool's column, Martin Gardner claimed that "e to the pi radical 163" is one of these. The Eisenstein ones are proper supersets that are extended with complex numbers. They form an Abelian group when endowed with addition and a commutative ring when endowed with addition and multiplication, but they are not a field, as they lack multiplicative inverses. As a set, they have cardinality "aleph 0", although they cannot be enumerated monotonically. The floor and ceiling functions yield, for 10 points, what type or numbers represented with a bold "Z," the set tha
In an April fool's column, Martin Gardner claimed that "e to the pi radical 163" is one of these. The Eisenstein ones are proper supersets that are extended with complex numbers. They form an Abelian group when endowed with addition and a commutative ring when endowed with addition and multiplication, but they are not a field, as they lack multiplicative inverses. As a set, they have cardinality "aleph 0", although they cannot be enumerated monotonically. The floor and ceiling functions yield, for 10 points, what type or numbers represented with a bold "Z," the set that is exactly the union of the natural numbers, their additive inverses, and zero.
In an April fool's column, Martin Gardner claimed that "e to the pi radical 163" is one of these.
integers