Show HN: I made a calculator that works over disjoint sets of intervals

1 sources1 storiesFirst seen 4/18/2026Score20Mixed Progress

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fouronnes3

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I've been studying interval arithmetic for the past few weeks and it's a really interesting field because while there is a ton of super interesting research published over the past decades, it has never really gotten the recognition that it deserves, IMO.One reason for this is that standard interval arithmetic has really poor handling of division by intervals containing zero.

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If you compute 1 / [-1, 2] in regular interval arithmetic, you get either [-∞, +∞], or you have to say that the operation is undefined.

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Both solutions are virtually useless.

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The real answer of course is [-∞, -1] U [0.5, +∞]: i.e.

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a union of two disjoint intervals.This is useful because you can confidently exclude a non empty set of the real numbers ([-1, 0.5]) from the set of possible values that you can get by dividing 1 by a number between -1 and 2.But this definition of interval division yields a value that is not an interval.

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A: I've been studying interval arithmetic for the past few weeks and it's a really interesting field because while there is a ton of super interesting research published over the past decades, it has never really gotten the recognition that it deserves, IMO.One reason for this is that standard interval arithmetic has really poor handling of division by intervals containing zero.

B: If you compute 1 / [-1, 2] in regular interval arithmetic, you get either [-∞, +∞], or you have to say that the operation is undefined.