RM = Raul Miller, DB = me

RM>  infinite digits are required.

DB>  Required for what application?

RM>  Complete accuracy in all contexts.

This is precisely the cop out to avoid.  Define your contexts.  Decide how many 
digits is enough.  Saying "I need infinite precision because that way I can be 
confident that my result is correct no matter how I obtain it" is precisely 
equivalent to saying "I give up".  

If you don't know how many digits you need, or how to obtain them, don't expect 
that the J interpreter or the IEEE council will.  The best you can hope for is 
that they'll provide many more than you require (i.e. an approximation of 
infinity).  If that turns out not to be the case, you've got some decisions to 
make and some debts to pay.

Or, alternatively:  divide the current size of the universe by the Planck 
length.  Use that many digits.  That's about as wide as your confidence 
interval can get.  Unfortunately, because the universe is open (not flat nor 
closed), you're going to constantly need more digits to be really sure.   And 
at an accelerating pace, to boot.  Damn those tricky gods.  

(on the other hand, if the tricky gods couldn't solve the continuity problem, 
we shouldn't feel so bad about our own failure)

-Dan
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