(Borrowed from the authors lecture on 2008)
You should know that every positive integer may be written in decimal notation:
Similarly, given any integer (``base'') , we may write a number as a string of digits in base . For example, we have
Similarly, we have
You may also probably know (repeating) decimal expresions of positive rational numbers.
Now let us reverse the order of digits. Namely, we employ a notation like this1:
Let us do some calculation with the above notation:
with our curious notation. Then do the same computation in the usual digital notation in base .