Foundations of Constructive Analysis
by Errett Bishop, Michael Beeson
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…solving the halting problem. It cannot be done. It turns out Cauchy sequences are better behaved, and (with a bit computational improvement) you can make a lot of things work out. See Bihshop's book, Foundations of Constructive Analysis, for details.
on “0.999...= 1” ↗…there is about 40-ish years into it Beltrami and then Klein started showing why hyperbolic geometry is interesting and important (per Milnor[0]). Constructive mathematics is older than that by now ('Foundations of Constructive Analysis' came out in 1967, and the field was old even then), where are its applications to other fields of math? By 'application' I'm meaning stuff like, for example, how certain isometries of the plane (PSL2(R))…
on “Computing an integer using a Grothendieck topos” ↗