

You know what all those methods have in common? FUCKING evaluation of smooth continuous functions based on a limited number of samples.
REAL MEN WRITE REAL PROOFS. They don’t use God damned computational methods which completely IGNORE non-converging regions.
I used opus to generate this lean-verifiable proof that you in particular are full of shit!
import Mathlib
open Real
noncomputable def f (x : ℝ) : ℝ := sin (π * x) * exp (-x^2)
lemma f_smooth : ContDiff ℝ ⊤ f :=
(contDiff_sin.comp (contDiff_const.mul contDiff_id)).mul
(contDiff_exp.comp (contDiff_id.pow 2).neg)
lemma f_zero_on_ints : ∀ n : ℤ, f n = 0 := by
intro n
show sin (π * (n : ℝ)) * exp (-((n : ℝ))^2) = 0
rw [mul_comm π (n : ℝ), sin_int_mul_pi, zero_mul]
lemma f_ne_zero : f ≠ 0 := fun h => by
have h₁ : f (1/2) = 0 := congrFun h (1/2)
have h₂ : f (1/2) = exp (-(1/2)^2) := by
show sin (π * (1/2)) * exp (-(1/2)^2) = exp (-(1/2)^2)
rw [show π * (1/2) = π/2 from by ring, sin_pi_div_two, one_mul]
exact (exp_pos _).ne' (h₂ ▸ h₁)
theorem sampling_is_a_lie :
∃ f : ℝ → ℝ,
ContDiff ℝ ⊤ f ∧
(∀ n : ℤ, f n = 0) ∧
f ≠ 0 :=
⟨f, f_smooth, f_zero_on_ints, f_ne_zero⟩



Yes, and I’m beginning to suspect that the group of people who don’t understand why they have an incompetent middle manager and the group who doesn’t get good results out of AIs has 100% overlap.
Please feel free to downvote me into oblivion.