链式箭头记号：修订间差异

2025年7月2日 (三) 03:46的版本

链式箭头记号(Chained arrow notation,别名康威链^[注])是由John Horton Conway和Richard K. Guy制作的高德纳箭头的推广记号。

$a \to b = a^{b}$

$a \to b \to c = a ↑^{c} b = a \underset{c}{\underset{⏟}{↑ \dots ↑}} b$

$a \to \dots \to b \to 1 = a \to \dots \to b$

$a \to \dots \to b \to 1 \to c = a \to \dots \to b$

$a \to \dots \to b \to (c + 1) \to (d + 1) = a \to \dots \to b \to (a \to \dots \to b \to c \to (d + 1)) \to d$

@@ 第2行： / 第2行： @@
 ==== 定义 ====
+<math>a \rightarrow b = a^{b}</math>
-==== <math>a \rightarrow b = a^{b}</math> ====
+<math>a \rightarrow b \rightarrow c = a\uparrow^cb = a\underbrace{\uparrow\ldots\uparrow}_c b</math>
-==== <math>a \rightarrow b \rightarrow c = a\uparrow^cb = a\underbrace{\uparrow\ldots\uparrow}_c b</math> ====
+<math>a \rightarrow\ldots\rightarrow b \rightarrow 1 = a \rightarrow\ldots\rightarrow b</math>
-==== <math>a \rightarrow\ldots\rightarrow b \rightarrow 1 = a \rightarrow\ldots\rightarrow b</math> ====
+<math>a \rightarrow\ldots\rightarrow b \rightarrow 1 \rightarrow c = a \rightarrow\ldots\rightarrow b</math>
-==== <math>a \rightarrow\ldots\rightarrow b \rightarrow 1 \rightarrow c = a \rightarrow\ldots\rightarrow b</math> ====
+<math>a \rightarrow\ldots\rightarrow b \rightarrow (c + 1) \rightarrow (d + 1) = a \rightarrow\ldots\rightarrow b \rightarrow (a \rightarrow\ldots\rightarrow b \rightarrow c \rightarrow (d + 1) ) \rightarrow d</math>
-==== <math>a \rightarrow\ldots\rightarrow b \rightarrow (c + 1) \rightarrow (d + 1) = a \rightarrow\ldots\rightarrow b \rightarrow (a \rightarrow\ldots\rightarrow b \rightarrow c \rightarrow (d + 1) ) \rightarrow d</math> ====