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erdos_350.variants.strengthening

Specification

If `A ⊂ ℕ` is a finite set of integers all of whose subset sums are distinct then `∑ n ∈ A, 1/n^s < 1/(1 - 2^(-s))`, for any `s > 0`. Proved by Hanson, Steele, and Stenger. We exlude here the case `s = 0`, because in the informal formulation then the right hand side is to be interpreted as `∞`, while the left hand side counts the elements in `A`.

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Lean 4 Statement
theorem erdos_350.variants.strengthening (A : Finset ℕ) (hA : DecidableDistinctSubsetSums A)
    (s : ℝ) (hs : 0 < s) : ∑ n ∈ A, (1 / n : ℝ)^s < 1 / (1 - 2^(-s))
ID: ErdosProblems__350__erdos_350.variants.strengthening
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