>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?

By "based" you mean what? Can any of them be written as 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),

47321/33461 is a good approximation to http://www.cut-the-knot.com/gifs/sqrt.gif";]2. But the two are not equal. Any real number can be approximate with arbitrary precision by rational numbers. Does it mean that every real number is rational. No, of course not.

>should this not also be
>seen as a rational number
>- Especially since in mathematics
>rational means "ratio like"??

Rational means being represented as a ratio, not "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!

You should be more careful using words in your arguments. [img src="http://www.cut-the-knot.com/gifs/sqrt.gif2 never approaches infinity. In fact it's a constant.

>Please enlighten me if I somehow
>got this wrong!

You may try getting help on the sci.math newsgroup. You may be able to get a more enlighten argumentation.