Money is mostly about the ratio function

Those big numbers on each and every cash bill have to obey a ratio formula. A ten is two fives and a twenty is two tens. The currency banker can only keep those ratios approximate, because prices need imprecision to adapt.  Digital currency does not help, digital coins still quantize. So money theory assumes a cotangent space, money is about smooth enough surfaces with reasonably defined perpindicuars  in a quantized integer field.