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posted by Fnord666 on Monday July 31 2017, @01:41PM   Printer-friendly
from the it's-a-rope-bridge dept.

Arthur T Knackerbracket has found the following story:

With a surprising new proof, two young mathematicians have found a bridge across the finite-infinite divide, helping at the same time to map this strange boundary.

The boundary does not pass between some huge finite number and the next, infinitely large one. Rather, it separates two kinds of mathematical statements: "finitistic" ones, which can be proved without invoking the concept of infinity, and "infinitistic" ones, which rest on the assumption — not evident in nature — that infinite objects exist.

Mapping and understanding this division is "at the heart of mathematical logic," said Theodore Slaman, a professor of mathematics at the University of California, Berkeley. This endeavor leads directly to questions of mathematical objectivity, the meaning of infinity and the relationship between mathematics and physical reality.

More concretely, the new proof settles a question that has eluded top experts for two decades: the classification of a statement known as "Ramsey's theorem for pairs," or RT22. Whereas almost all theorems can be shown to be equivalent to one of a handful of major systems of logic — sets of starting assumptions that may or may not include infinity, and which span the finite-infinite divide — RT22 falls between these lines. "This is an extremely exceptional case," said Ulrich Kohlenbach, a professor of mathematics at the Technical University of Darmstadt in Germany. "That's why it's so interesting."

The abstract is available on arXiv — the full article is available as a pdf.

[Ed note: Not a new story but interesting and will hopefully spark some discussion.]

-- submitted from IRC


Original Submission

 
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  • (Score: 1, Redundant) by epitaxial on Tuesday August 01 2017, @11:36PM (4 children)

    by epitaxial (3165) on Tuesday August 01 2017, @11:36PM (#547782)

    Say it again with me. Take pie and divide it into 0 pieces. What are you left with?

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  • (Score: 1, Redundant) by Wootery on Wednesday August 02 2017, @08:47AM (2 children)

    by Wootery (2341) on Wednesday August 02 2017, @08:47AM (#547880)

    How many times do I have to say it? The question makes no sense. It's like asking How many angels can dance on the head of a pin?

    I have already spelled out in length why your idea doesn't work.

    • (Score: 0) by Anonymous Coward on Friday August 04 2017, @12:12AM (1 child)

      by Anonymous Coward on Friday August 04 2017, @12:12AM (#548528)

      Sorry for the mismoderation, it's #547782 that's redundant.

      • (Score: 2) by Wootery on Friday August 04 2017, @08:33AM

        by Wootery (2341) on Friday August 04 2017, @08:33AM (#548649)

        Apparently not... did you not see epitaxial's comment?

  • (Score: 2) by Wootery on Friday August 04 2017, @08:35AM

    by Wootery (2341) on Friday August 04 2017, @08:35AM (#548650)

    Actually, I take back what I said about corresponding with the intuitive idea of division. We extend division to non-integer quotients, and we happily divide negative numbers, complex numbers, etc, but that's hardly intuitive in terms of pies.

    None of those 'extensions' have the problems that your suggestion has, though.