ข้อพิสูจน์ ของ ลิมิตของลำดับ

  1. ↑ Proof: choose N = 1 {\displaystyle N=1} . For every n ≥ N {\displaystyle n\geq N} , | x n − c | = 0 < ϵ {\displaystyle |x_{n}-c|=0<\epsilon }
  2. ↑ Proof: choose N = ⌊ 1 ϵ ⌋ {\displaystyle N=\left\lfloor {\frac {1}{\epsilon }}\right\rfloor } + 1 (the floor function). For every n ≥ N {\displaystyle n\geq N} , | x n − 0 | ≤ x N = 1 ⌊ 1 / ϵ ⌋ + 1 < ϵ {\displaystyle |x_{n}-0|\leq x_{N}={\frac {1}{\lfloor 1/\epsilon \rfloor +1}}<\epsilon } .

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