User:Johnwaylandbales/sandbox

The 1=(1,0) is not forced if one equates a real number x with the sequence x,0,0,0,. . . and equates the ordered pair (x,y) of two sequences x0,x1,x2,. . . and y0,y1,y2,. . . with the shuffled sequence x0,y0,x1, y1,. . . . In this context, 1=(1,0) and one has, for the basis vectors e0=1, e2k=(ek,0) and e2k+1=(0,ek).