User blog comment:Simplicityaboveall/The Construction of Extremely Large Numbers/@comment-24920136-20160725013617/@comment-1605058-20160728200603

Another problem is that numbers can be written in terms of 10's in many different ways. For example, number 110 can be written as 10^2+10, which leads us to w^2+w, but we can also write it as 10+...+10 (eleven 10's), which only leads us to w*11. Of course, you might think of this as a rather silly example because [insert a reason here], but I only want to illustrate a point - you need to exactly specify what you mean by "COMPLETE HEREDITARY FORM OF m to base n", and, if possible, convince us that this FORM always exists and is unique for every single m.