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Life & fun · April 18, 2026

IM

I made a calculator that works over disjoint sets of intervals

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. If you compute 1 / [-1, 2] in regular interval arithmetic, you get either [-∞, +∞], or you have to say that the operation is undefined. Both solutions are virtually useless. The real answer of course is [-∞, -1] U…

I made a calculator that works over disjoint sets of intervals launched on April 18, 2026 with 314 votes, #64 of 21,248 launches that month and more than 99% of that year's launches.

In plain words

This is a calculator that performs arithmetic operations on disjoint sets of intervals, addressing a key limitation in standard interval arithmetic. It's designed for mathematicians and researchers studying interval arithmetic who need more precise results when dividing by intervals containing zero. The tool returns unions of disjoint intervals rather than unbounded or undefined results, allowing users to confidently exclude ranges of real numbers from possible outcomes. It's built on interval arithmetic research that the creator believes deserves broader recognition in computational mathematics.

written from the facts on this page · September 2026

From the sources

This is a calculator that works over unions of intervals rather than just real numbers. It is an implementation of Interval Union Arithmetic . An interval [a, b] represents the set of all numbers between and including a and b. An interval union: [a, b] U [c, d] is a disjoint set of intervals. ➤ 2 / [-2, 1] [-∞, -1] U [2, +∞] The interesting thing about interval union arithmetic is the inclusion property, which means that if you pick any real number from every input union and compute the same expression over the reals, the result is guaranteed to be in the output union. ➤ ( [5, 10] U [15, 16] ) / [10, 100] [0.05, 1.6] Operations can result in disjoint unions of intervals: ➤ 1 / [-2, 1] [-∞,…from victorpoughon.github.io

In the maker’s words, at launch

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…

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