Real numbers are sequences of integers which are infinite in one direction. If I have a string which is infinite in both directions, say ...345123985..., then I can form an injection from these strings to R^2 and then into R (just pick a point and read of a real number for both direction), is there any simple surjection from R to these doubly infinite strings?
Is there any context in which these numbers arise or have any use?
I consider two strings equal if they are equal after a translation. Is there any way to define an order-relation on them ?