Question

Let Mi be the set of all sequences {a.);, of real num bers such that Σ converges. More formally, we could write this as 1 lal M1a :(W) ai R and i=1 We introduce a function p: Mi x MiR by setting 95 Let (Mi,p) denote the particular metric space we introduced above, and for each X = {xīた1 e M and for each i, we refer to the number xi as the ith coordinate of X. For each N EN, let XiN denote the element of Mi which has the same first N coordinates as X, but all of whose coordinates after the Nth coordinate are zero. We could write this more formally as i=1 where, for each n Vi=Įxī, if i N Let X E M. Prove that the sequence X NN converges to X (in (M1.ρ.) ).

Answer 1

仁「 ˋ一.FBY. ν.0m e7 о 곰 KeN such +ask I2K