Let $f:ℝ→ℝ$ be a real analytic function. Assume that $f$ has infinitely many zeros. Let $D$ be the set of those zeros. Prove that $D$ is bijective with the integers set $ℤ$.
2026-05-05 20:25:13.1778012713
Prove that $D$ is bijective with the integers set $ℤ$
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If $f=0$, $f$ is analytic and $D$ is uncountable. Otherwise, $D$ is a discrete set; because $\mathbb{R}$ is separable, $D$ is at most countable.