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Mathoverflow.net news digest

  • 9 years

    Rule for Finding Largest Possible Perimeter

    Some months ago I was given a high-school level maths question that made me wonder if there was a definitive principle for finding the shape of largest perimeter given a set of dots. The question was worded something like the following; Given a 5 by...

  • 14 years

    Hartogs number and the three power sets

    One of the most important constructions in ZF+$\lnot$AC is Hartogs number, defined as:
    $$\aleph(X)=\min\lbrace\alpha:|\alpha|\nleq|X|\rbrace$$
    We can prove that this ordinal always exists in the following way:

  • 0 days

    How much can we do better in sphere packing by decreasing sphere sizes?

    One variant of the traditional sphere packing problem in $\mathbb R^3$ asks what the density $\rho_r$ of spheres of equal radii $r$ one can fit in a unit cube without exceeding the boundary asymptotically as $r$ goes to 0. It is known that a packing...

  • 0 days

    Do Robinson's non-standard numbers undermine Godel's argument

    Godel's incompleteness argument depends on modelling mathematical proof inside the system under consideration. The intuition is that the statements in an argument can be indexed by natural numbers and the characters in a statement can also be indexed...

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