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A comment on Toward an API for the Real Numbers. Parent comment

Re:Toward an API for the Real Numbers by _ouml_ on Wednesday October 07, 2020 @12:35AM (#24705338)
The equality test is equivalent to deciding if something is 0. You can probably ask the app to calculate sqrt(2) * sqrt(2). If that doesn't show a 2 as answer, you've lost. Same goes for sin(arcsin(1/2)). You want the exact answer.
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Re:Toward an API for the Real Numbers by H8crilA on Wednesday October 07, 2020 @05:42AM (#24706619)
Equality is also needed if you want to know whether "x<y".

Proof: 1) suppose you can decide whether "x<y" for all x,y. 2) Then, for all x,y you can decide whether x==y because that's just "!(x<y) && !(y<x)"

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