Real Analysis For each n in the positive integers, let P n = be a point in R 2 . Show that {P n } from n=1 to infinity converges to P= in R 2 if and only if {x n } from n=1 to infinity and {y n } from...

Real Analysis

For each n in the positive integers, let P_n=<>_n,y_n> be a point in R². Show that {P_n} from n=1 to infinity converges to P= in R²
if and only if {x_n} from n=1 to infinity and {y_n} from n=1 to infinity converge in R¹
to x and y respectively.

Please be thorough in your answer, explaining each portion to me.  Thank you.