Another amazing work by Hans Boehm back in 1999: a constructive real number calculator, https://www.hboehm.info/crcalc/ . In a sense, this is "as far as a computer can go" in the hierarchy of accuracy that includes floating-point, exact rational numbers, and then constructive reals.
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Which proverbially depends on what the definition of “is” is.
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Vaguely related: The other day I was reading up on Risch's algorithm which is the basis for many practical integration algorithms. But nobody knows if it really is a true algorithm because it relies on equality testing in a domain where nobody has proved equality is decidable.
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Incidentally, here's a modern rewrite-based symbolic integrator which isn't based on Risch: https://rulebasedintegration.org/
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Hey, Mrs. Abend ... tweet out to Tim Sweeney again this year (you RTed one of my student's Halloween costumes last year and it made him famous at school - he dressed as you) maybe he will donate to our fundraiser. So, here goes ... as requested:https://charity.gofundme.com/o/en/campaign/projectextra …
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