ω 生成策梅洛序数Generate Zermelo Ordinals

使用说明与常见问题How-to & FAQ

「生成策梅洛序数」是什么？What is the Generate Zermelo Ordinals tool?

生成策梅洛自然数的集合写法：0=∅, 1={∅}, 2={{∅}}, 3={{{∅}}}, …。可指定从 0 到 N。本地处理。Generate Zermelo naturals in set notation: 0 = empty set, 1 = singleton of empty, 2 = singleton of that, and so on, from 0 through N. Processed locally.

如何使用「生成策梅洛序数」？How do I use the Generate Zermelo Ordinals tool?

在「生成策梅洛序数」中，按需设置「最大 N」，结果会实时显示在下方，点击「复制结果」即可复制。Enter "Max N" and the page lists the Zermelo ordinals 0 to N in set notation, where each number is the set containing only the previous one (0 is the empty set). Click "Copy result" to copy the list.

和冯·诺依曼序数有何不同？How does this differ from von Neumann ordinals?

策梅洛用单元素嵌套集合表示后继；冯·诺依曼用前面所有序数的集合。策梅洛写法更短。Zermelo uses a single nested singleton for the successor; von Neumann uses the set of all previous ordinals. Zermelo notation stays shorter.

N = 0 会输出什么？What does N = 0 give?

只输出一行「0 = ∅」；最大 N 为 100。结果是纯文字（逐位处理），不涉及浮点计算。Just one line, 0 = ∅; Max N is 100. The result is plain text (processed as text) with no floating-point arithmetic.

输入和输出是什么样的？What does the input and output look like?

例如在「生成策梅洛序数」中把「最大 N」设为 3，输出为：0 = ∅ ⏎ 1 = {∅} ⏎ 2 = {{∅}} ⏎ 3 = {{{∅}}}（⏎ 表示换行）。For example, in the Generate Zermelo Ordinals with "Max N" set to 3, the output is: 0 = ∅ ⏎ 1 = {∅} ⏎ 2 = {{∅}} ⏎ 3 = {{{∅}}} (⏎ marks a line break).

有哪些选项可以调整？What options can I adjust?

「生成策梅洛序数」的设置：「最大 N」默认 5。改动任一选项后结果会按新设置重新生成。Settings in the Generate Zermelo Ordinals — "Max N" default 5. Changing any option regenerates the result with the new setting.

「生成策梅洛序数」免费吗？需要注册吗？Is the Generate Zermelo Ordinals free? Do I need an account?

「生成策梅洛序数」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Generate Zermelo Ordinals is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.