On 19 Jun., 05:10, Virgil <Vir...@home.esc> wrote: > In article
> > It is. Every real number that is defined is defined by a finite word > > (definition or formula). It is impossible to define a number by an > > infinite sequence, because the sequence never ends and the definition > > is never known. > > F:N -> R: n -> 3/10^n is an infinite sequence defining a real number.
No, "F:N -> R: n -> 3/10^n" is a finite rule *producing* an infinite sequence! > > So as one can easily see it is possible to have an infinite sequence > defining a real number. > > In real mathematics, an infinite sequence is merely a function whose > domain is the set of natural numbers, and there are lots of them which > define real numbers.
There is none. But you are not able to grasp the difference between an infinite sequence and the rule producing that sequence.
Sorry, but if you cannot think so far, then further discussion is meaningless.