Dear Alex,
You write that a number r is rational if it can be written a fraction r = p/q where both p and q are integers.
Does that mean that phi - = "The golden section", "The golden ratio", "The divine proportion" - should be considered rational, as the number phi = r obviously is based upon r = p/q?

Also, if ?2 likewise can be written as r = p/q, as for example r = 47321/33461 = ?2, (where 33461 = prime and 47321 = prime 599 x prime 79), should this not also be seen as a rational number - Especially since in mathematics rational means "ratio like"?? Note that the ?2 behaves in exactly the same manner as phi, i.e. as it approaches infinity it becomes what it is!

Please enlighten me if I somehow got this wrong!
Kind regards
Klaus Kastberg.