On 9 Jan., 10:16, Virgil <vir...@ligriv.com> wrote:
> > A real number is determined or "given" by a unique word. > > No number is given by a single word until that word has been defined as > meaning some number.
> > > Otherwise it > > could not be used. > > Many, if not most, numbers are referred to by numerals which are at > least grammatically more like phrases rather than single words.
Every finite string of symbols is a word. This includes Shakespeares collected works as well as the number 1. > > > And it was not possible to compare some finite > > initial segment of it with something else. > > I can compare 3.14159 with a lot of things.
But you are not bright enough to understand that you have used a rational number defined by a single word. And if you meant it as an approximation of pi that eventually has to be improved, then you need a definition of pi, i.e., a finitely defined way to obtain better approximations.