以下是denumerable与countable的用法辨析:
1. 数学语境差异:
- denumerable(可数的)特指与自然数集等势的无限集合(即??基数),强调"可枚举性"
例:The set of integers is denumerable but infinite.
- countable(可数的)包含两种含义:
a) 有限集合
b) 与denumerable同义的无限可数集
例:Any finite set is countable by definition.
2. 词源特征:
- denumerable来自拉丁语"denumerare"(逐一数清),隐 ...(以上内容有节略,please sign in for more)
Finite or countably infinite; having a one-to-one correspondence (bijection) with a subset of the natural numbers.
Countably infinite; having a bijection with the natural numbers.
Freely usable with the indefinite article and with numbers, and therefore having a plural form.
Capable of being assigned a bijection to the natural numbers. Applied to sets which are not finite, but have a one-to-one mapping to the natural numbers.
Finite or countably infinite; having a one-to-one correspondence (bijection) with a subset of the natural numbers.
Countably infinite; having a bijection with the natural numbers.
Freely usable with the indefinite article and with numbers, and therefore having a plural form.
Capable of being assigned a bijection to the natural numbers. Applied to sets which are not finite, but have a one-to-one mapping to the natural numbers.