Maybe this will prove useful to someone.

Viewing Numbers, esp. the rationals, as singularities has never appealed to me.
Have always felt they are way more like toroids than singularities hence the abs.

Sort of like "fuzzy" comparisons, i.e. is a point,X, with center,x, and radius, Ri, anywhere or completely within the range of point,Y, with center, y, and radius Rj.

Ciao. Peace and Music thru us all,