Section 11.6: fix Summable indexing and Exercise 11.6.4 statements#527
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`Summable f` with `f : ℝ → ℝ` sums over the index type ℝ, which makes these statements unprovable: a nonnegative function with uncountable support is never summable over ℝ, so e.g. `f x = 1/(1+x)^2` satisfies the bounded-integral side of Proposition 11.6.4 but not the summable side. The integral test of the text concerns the series over the natural numbers, so the intended statement is `Summable (fun n:ℕ ↦ f n)`. Also restate the Exercise 11.6.4 examples with nonnegativity as a conjunct `(∀ x ≥ 0, f x ≥ 0) ∧ ...` rather than a named existential binder: the book asks for counterexamples satisfying all hypotheses of the integral test except monotonicity, and the binder form triggers unused-variable warnings once the proofs are filled in. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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Summable fwithf : ℝ → ℝsums over the index type ℝ, which makes these statements unprovable, so the intended statement isSummable (fun n:ℕ ↦ f n).Also restate the Exercise 11.6.4 examples with nonnegativity as a conjunct
(∀ x ≥ 0, f x ≥ 0) ∧ ...rather than a named existential binder: the book asks for counterexamples satisfying all hypotheses of the integral test except monotonicity, and the binder form triggers unused-variable warnings once the proofs are filled in.