How many real numbers exist? New proof moves closer to an answer

Re:How many real numbers exist? New proof moves closer to an... by gorgoiler on Thursday July 15, 2021 @12:37PM (#27846673)

We don’t know but looking into the past hints at the future.

Cantor, Hilbert and Gödel gave us Church who gave us Turing. Turing and Flowers gave us the machines as well as the theory. All of them put together gave us type systems and types are how you formally prove that your 747 software is free of, if not all bugs, then at least certain large classes of error.

There is a clear line of connections from Cantor (1890s) to jumbo jet fly-by-wire (1990s.)

Countability of sets and Cantor’s diagonal argument — the subject of the first part of this article — are some of the first topics teenagers learn about in high school CS (if you’re lucky and on a very modern course) or CS101 (if you’re at a University.) Types are sets.

Who knows what today’s mathematics will bring us in the year 2121?

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Re:How many real numbers exist? New proof moves closer to an... by lupire on Thursday July 15, 2021 @01:44PM (#27847565)

Eh, this argument kind of falls apart with higher infinities, where the numbers you are studying are bigger than the power set of all interactions among all particles in all possible universes.

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Re:How many real numbers exist? New proof moves closer to an... by mmastrac on Thursday July 15, 2021 @01:07PM (#27847008)

I'd love to see James Burke tackle this line.

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