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Input and interpretation of Intervals with machine-precision bounds

  • To: mathgroup at
  • Subject: [mg86300] Input and interpretation of Intervals with machine-precision bounds
  • From: "Andrew Moylan" <andrew.j.moylan at>
  • Date: Sat, 8 Mar 2008 05:39:00 -0500 (EST)

How can I input the Interval representing all numbers between the
machine-representable number 3. and the machine representable number 4.?

  Interval[{3., 4.}] // InputForm
  Interval[{2.9999999999999996, 4.000000000000001}]

Note that re-entering this //InputForm output widens the interval even
further again:

  Interval[{2.9999999999999996, 4.000000000000001}] // InputForm
  Interval[{2.999999999999999, 4.000000000000002}]

It's strange that entering the InputForm doesn't recover the original
expression! Is this by design?

Here's one way to obtain the Interval between 3. and 4.:

  Interval[{3.0000000000000004, 3.9999999999999996}] // InputForm

In other words, one can pre-empt Mathematica's widening of the interval by
contracting it. But this doesn't leave us with any way of obtaining
Interval[{3., 3.}]. This seems strange since Interval[{3, 3}] is an
acceptable interval.

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