CantorStaircase
CantorStaircase
给出康托尔阶梯函数 
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更多信息
- 康托尔阶梯函数也称作康托尔三分函数，或康托尔函数.
- 数学函数，适宜于符号和数值运算.
- 对于
，康托尔函数等于 ![TemplateBox[{x}, CantorStaircase]=sum_i2^(-n_i)](Files/CantorStaircase.zh/1.png "TemplateBox[{x}, CantorStaircase]=sum_i2^(-n_i)")
. - 对于某些参数，CantorStaircase 自动运算至精确值.
- CantorStaircase 能运算至任意数值精度.
- CantorStaircase 自动逐项作用于列表的各个元素. »
范例
打开所有单元 关闭所有单元基本范例 (2)
CantorStaircase[1 / 3]在单位区间上绘制 CantorStaircase：
Plot[CantorStaircase[x], {x, 0, 1}]范围 (13)
数值运算 (5)
CantorStaircase[0.76]CantorStaircase[0]CantorStaircase[15 / 17]N[CantorStaircase[1 / Sqrt[2]], 20]CantorStaircase[{{1 / 2, 0}, {0, 1 / 2}}]或用 MatrixFunction 计算矩阵形式的 CantorStaircase 函数：
MatrixFunction[CantorStaircase, {{1 / 2, 0}, {0, 1 / 2}}]//FullSimplify函数的属性 (8)
CantorStaircase 对所有实数有定义：
FunctionDomain[CantorStaircase[x], x]FunctionDomain[CantorStaircase[x], x, Complexes]CantorStaircase 的值域：
FunctionRange[CantorStaircase[x], x, y]FunctionSurjective[CantorStaircase[x], x]Plot[{CantorStaircase[x], 2}, {x, -2, 2}]CantorStaircase 不是单射函数：
FunctionInjective[CantorStaircase[x], x]Plot[{CantorStaircase[x], 1}, {x, -2, 2}]CantorStaircase 是连续的：
FunctionContinuous[CantorStaircase[x], x]CantorStaircase 非递减：
FunctionMonotonicity[CantorStaircase[x], x]CantorStaircase 非负：
FunctionSign[CantorStaircase[x], x]CantorStaircase 既不凸，也不凹：
FunctionConvexity[CantorStaircase[x], x]TraditionalForm 格式：
CantorStaircase[x]//TraditionalForm
Wolfram Research (2014)，CantorStaircase，Wolfram 语言函数，https://reference.wolfram.com/language/ref/CantorStaircase.html.
文本
Wolfram Research (2014)，CantorStaircase，Wolfram 语言函数，https://reference.wolfram.com/language/ref/CantorStaircase.html.
CMS
Wolfram 语言. 2014. "CantorStaircase." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/CantorStaircase.html.
APA
Wolfram 语言. (2014). CantorStaircase. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/CantorStaircase.html 年