The Real Number System

Definition Let r be a real number A sequence i∈N of real numbers converges to r if, for every ε>0, there is an N such that for every i≥N, ri−rε

Ernest William Hobson corresponding real numbers in the new aggregate of real numbers number , which we may denote by a Two such aggregates { a } , { b }

real fake It is thought that the first real number to be identified as irrational was discovered by the Pythagoreans in the sixth century BC Prior to this discovery,

realms Ernest William Hobson corresponding real numbers in the new aggregate of real numbers number , which we may denote by a Two such aggregates { a } , { b }