#duodecimal system

MY ALGEBRALIEN OC

my oc. pls treat it kindly. credit if used. she/it

17, obviously.

Today we will count the rational numbers. The rational numbers, those are the numbers that can be written as a fraction of whole numbers. That can be done in many ways, for example the fractions 1/2, 2/4, 3/6, 4/8, … all represent the same number. For every rational number we choose the fraction with the smallest possible numerator and denominator (and whole numbers get denominator 1). So, from the above sequence of fractions only 1/2 remains. Furthermore, in case the rational number is negative, we put the minus sign in front of the fraction. Thus, we write -1/2 and not 1/(-2).

Now we perform a nice trick: we read the minus sign and the slash as digits. How? By working in the duo-decimal system. We replace the -, when present, by A and the / by B. In the duo-decimal system the A is the digit for `ten' and the B represents `eleven'. For example, 1/2 becomes 1B212 (the 12 indicates that we work duo-decimally). In the decimal system we get 1×144+11×12+2×1=27810, that natural number corresponds to 1/2 (the 10 indicates decimal representation). The natural that goes with -1/2 is A1B212 and that becomes 10×1728+1×144+11×12+2×1, or 1755810. Calculate for yourself which natural numbers go with 0/1, 1/1, and -1/1.