The union of intervals defined by the set A_n = (n − 1, n + 1) for all natural numbers n is represented as ∪_{n≥1}A_n. This union encompasses all real numbers from 0 to infinity, specifically expressed as (0, ∞). Each interval A_n contributes to the overall union, and the proof involves demonstrating that every real number greater than 0 is included in at least one of these intervals.
PREREQUISITESStudents in mathematics, particularly those studying real analysis, set theory, or preparing for advanced calculus. This discussion is beneficial for anyone seeking to understand the concept of unions of intervals and their implications in mathematical proofs.
James Brady said:Homework Statement
Let ##A_n = (n − 1, n + 1)##, for all natural numbers n. Find, with proof, ##∪_{n≥1}A_n##
Homework Equations
What does that last statement mean? Union for n greater than or equal to one times the interval?
The Attempt at a Solution
I can't understand the question.