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[Alex K]

Jesus GC, you of all people should appreciate the fact that pi is the exact ratio for an idealized perfect circle which can be mathematically defined precisely, but never realized in nature. That's as transcendent as human thought gets.

Please explain how it can be exact when the number has no end.

GC

It cannot be represented exactly all at once using the decimal system for the reason you mention. Nevertheless, we can define the object Pi exactly mathematically, for example:

The number pi is defined as the second zero of the solution to the differential equation

f''(t)= -f(t)

with initial value f(0)=0 .

and we can even specify an algorithm how to calculate (in principle) any desired decimal place. In this sense, no part of pi is hidden from us.