Consider Rm ={(:1:0,:121,...) :333' E R} the vector space of countably infinite sequences of reals. We define the following maps: L($0,$1,$2,...) =(m1,:1:2,...) R($0,$1,$2,...) = \"1,320,231,322,\" .) 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? Update: Changed the subscripts of 1:;- so that they're increasing