若 ∀n∈N+,[an+1,bn+1]⊂[an,bn]\forall n \in \mathbb N_+, [a_{n+1}, b_{n+1}] \subset [a_n, b_n]∀n∈N+,[an+1,bn+1]⊂[an,bn], 且有 limn→∞(bn−an)=0\lim_{n \to \infty} (b_n - a_n) = 0limn→∞(bn−an)=0 ⟹ ∃!ξ,∀n∈N+,有an≤ξ≤bn\implies \exists! \xi, \forall n \in \mathbb N_+, 有 a_n \leq \xi \leq b_n⟹∃!ξ,∀n∈N+,有an≤ξ≤bn 也就是 ξ∈∩n=1∞[an,bn]\xi \in \mathop{\cap}\limits_{n=1}^\infty [a_n, b_n]ξ∈n=1∩∞[an,bn]
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