概念---数学分析2:常用概念汇总(完备性,柯西序列等...)

数学基础常用概念汇总

  • 完备性(Completeness)
  • 更多概念待更新~

完备性(Completeness)

Purpose:
它最初是用来表述,实数轴上没有洞,或者,没有间断点。
Cauchy completeness
Cauchy completeness is the statement that every Cauchy sequence of real numbers converges(From Wiki).

其中
Cauchy sequence
There is a sequence, x 1 , x 2 , x 3 , . . . x_1,x_2,x_3,... x1,x2,x3,...It is a Cauchy sequence if for every positive real number ε \varepsilon ε, there is a positive integer N N N such that for all natural numbers m , n > N m, n > N m,n>N, ∣ x m − x n ∣ < ε |x_m-x_n|<\varepsilon xmxn<ε

更多概念待更新~

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