Computers should have a more accurate representation of real numbers

Interesting idea - and well worth raising.

Perhaps related (but also a little different) is Interval Arithmetic. Just set your precision, do your calculations, and you end up with an upper and lower bound (for the given precision/inputs) - within which the exact value lies.

I've played with a C library, and a perl extension (that I wrote) that wraps that C library .... but only *played*.

Cheers,
Rob

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Re^2: Irrational numbers
by grondilu (Friar) on Dec 18, 2012 at 12:03 UTC

I would almost certainly need that. To display the result up to a certain accuracy, I assumed in the code above that the distance between two consecutive terms gets smaller and smaller. It's always possible to find a subsequence with such a property so we can define all reals as such.

I'm not sure this property is conserved with the arithmetic operations as defined above. So I would need a rigorous way of dealing with the sum or product of terms whose precision is known up to a given accuracy.

So: thanks, that'll be useful if I ever want to implement this thing for real.