Consider R = {(x0, 1,...): x < R} the vector space of countably infinite sequences of reals. We define the following maps: L(x0, 21, 22,...) = (x,x2,...) R(x0, x1,x2,...) = (0, x0, x1,x2,...) we call L the left shift transformation and we call R the right shift transformation. 1. Prove that L is onto but not one-to-one. 2. Prove that R is one-to-one but not onto. 3. Why are these transformations special? Could such maps exist for a finite dimensional space?