For ten points, name these numbers, which include 1,2,3,4... and often zero, a set of numbers often abbreviated N.
Russell defined them by defining a function that established a set consisting of x union y, where x belonged to the set being operated on and y was not an element of x. A well ordering can be defined on these based on subset relation in the usual construction. It can be defined by starting with the empty set and using the power set operator to establish a successor function, and when the axiom of infinity is used this represents the smallest such infinite set. Hence, the size of this entity is aleph naught. The integers can be defined as equivalence classes of these entities added together, and any finite amount of data can be coded into them based on the prime factorization theorem. For ten points, name these numbers, which include 1,2,3,4... and often zero, a set of numbers often abbreviated N.
Russell defined them by defining a function that established a set consisting of x union y, where x belonged to the set being operated on and y was not an element of x. A well ordering can be defined on these based on subset relation in the usual construction.
{natural} numbers