[edsheppa]

Oh, so you do know. Well that's more hopeful. But you think rational arithmetic is closed under that operation? Tell you what. Run this script, which as you can has nothing but rational arithmetic. I wonder if you will recognize the irrational number that is the limit. (Hint: it displeased a famous Greek.)

var x = 1
for (var i = 0; i < 1000; ++i)
{
    x = 1 + x;
    x = 1 / x;
    x = 7 * x;
    x = x / 4;
}
WScript.Echo(x + 1 / 2);

[HiTech RedNeck]

you old square rooter

[Fester Chugabrew]

(Hint: it displeased a famous Greek.)

Achilles?

[AndrewC]

The calculation terminates. The result is a rational number truncated to the accuracy of the machine on which the program is implemented. 1000 is a bit short of limitless.