Let An 0 n 1n x R 0 lessthanorequalto x SolutionBy defini

Let A_n = [0, n - 1/n] = {x R 0 lessthanorequalto x

Solution

By definition, A₂ = [ 0, ½), A₃ = [ 0, 2/3) , A₄ = [ 0, ¾) and so on. It may be observed that A_n A_n+1 for each n 2. Further, A₁ has not been defined explicitly.

Then A = A₁U A₂ UA₃ …… =    lim(A₁U A_n) as n = A₁ U [ 0,) Thus A is the entire positive part of the real number line including 0 plus A₁.