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Might one of the following examples work?

The Riemann hypothesis asserts that the real part of every non-trivial zero of the Riemann zeta function $ζ (s) = \sum_{n = 1}^{\infty} \frac{1}{n^{s}}$ is equal to $\frac{1}{2}$ .

(Stealing from Wikipedia): A sequence of groups and group homomorphisms $G_{0} f_{1} - \to G_{1} f_{2} - \to G_{2} f_{3} - \to \dots f_{n} - \to G_{n}$ is called exact if $im (f_{k}) = ker (f_{k + 1})$ for $0 \leq k < n$ .

(Also paraphrased from Wikipedia): Given an $n \times n$ matrix $A$ whose elements are $a_{i, j}$ , we can define the determinant $det (A) = \sum_{σ \in S_{n}} sgn (σ) \prod_{i = 1}^{n} a_{i, σ_{i}}$ where $S_{n}$ is the symmetric group on $n$ elements.

I'm a bit worried, though, that "standard research no... (read more)

Uncountability

Jason Gross9y*50

Thanks!

A^B is the set of functions from B to A. So 2^N is powerset of N (a function f from N to {0, 1} says, for each element of N, whether or not that element is in the subset defined by f), which is isomorphic to the reals. Perhaps this should go somewhere in one or more of the versions. I don't know any connection between this and P=NP (although I suppose it could be behind the exponential bounds on various things).

Jason Gross9y*13

LESSWRONG
LW

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