On 6/3/2014 12:26 AM, John Gabriel wrote: >> On Tuesday, 3 June 2014 02:36:11 UTC+2, Virgil wrote: > >> The enumeration of the rationals lasts forever. > > That's really funny. If the enumeration lasts forever, then it can never be completed, in which case, is it ever possible to call it an enumeration? > > It's like 0.333... When does it ever become 1/3? Never, because the 3s go on *forever*. > > See Virgil, nothing goes on forever. There is no such thing as forever or infinity or infinitely small or any other nonsense. >
Get off. One third is also written 1/3 and 0.333.... Actually, it's written 3 overbar, point three with the line over the repeating part instead of 0.33(3)....
Furthermore it is clear the exact value at a place of a rational number, to infinity.
Also for any irrational number as it is so defined, it is so.