In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> 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. > > Just so.
Then no number is "given" by a word until that word as been given the 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.
So that, at least in your mind, the collected works of Shakespeare are just one word? > > > > > 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.
What I have used is a finite initial segment for the infinite sequence of characters representing pi, a sequence of characters which is not even a number unless I intend it to be.
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.
One can finitely define infinite processes, like Archimedes method of approximating pi, but that does not make those processes finite. --