Notice that Mathematica refuses to tell us anything about the value of Pi. In
effect, it tells us that Pi is Pi. Why is that?

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Any number with a finite number
of digits that it printed out as the value of Pi would be an approximation,
since Pi has an infinite number of digits. Instead, it just tells us that Pi
is Pi. (It would be really slick if there were Greek letters on the computer
keyboard so that we could type the Greek symbol for Pi as input.)