For 10 points, name this set of numbers symbolized Z which includes 0, the natural numbers, and their negatives.
According to Gauss's Polynomial Theorem, a reducible polynomial with coefficients of this type can be factored into two polynomials with coefficients of this type. The Gaussian numbers of this type include a complex part, and a ring with no zero divisors is known as this type of domain. Leopold Kronecker hoped to ground analysis entirely in this set of numbers. This set can be extended from a smaller one by including the (*) additive inverses of successors to zero as defined by the Peano axioms. The floor and ceiling functions output a number of this type, and every rational number is a quotient of two of these numbers. For 10 points, name this set of numbers symbolized Z which includes 0, the natural numbers, and their negatives.
According to Gauss's Polynomial Theorem, a reducible polynomial with coefficients of this type can be factored into two polynomials with coefficients of this type.
{integers} [accept word forms; accept {Z} before mentioned]