葛立恒数是几位数（葛立恒数后面是什么）

你知道后继数运算吗？

后记数运算符号 +^{+} ， n+=n+1n^{+}=n+1

那我后继 22 次？ n++=(n+)+=n+1+1n^{++}=(n^{+})^{+}=n\!+\!1\!+\!1

后继 33 次？ n+++=((n+)+)+=n+1+1+1n^{+++}=((n^{+})^{+})^{+}=n\!+\!1\!+\!1\!+\!1

后继 mm 次？ n++…++n^{++…++} ( mm\! 次) =(((…(n+)…)+)+)+=(((…(n^{+})…)^{+})^{+})^{+} (m(m 个 +)^{+})

到了后继 mm 次的阶段，我们就可以换个符号 :+:+

上面那个数可以写作 n+mn\!+\!m 称作 nn 加 mm

那……加两次nn ？ n+n+nn+n+n

加三次？ n+n+n+nn+n+n+n

加 mm 次？ n+n+n+……+n+n+nn+n+n+……+n+n+n (m(m 次 ))

再换个符号？ :×:\times

上面那个数就可以用这种"×\times "来表示的运算写作 n×mn\times m

我们可以按照上面的规律不难得出 n×n×n×……×n×n×nn\times n\times n\times ……\times n\times n\times n 这个数

再定义乘方： nm=n×n×……×n×nn^{m}=n\times n\times ……\times n\times n

我们就可以介绍二号男主角：高德纳箭头 ↑\uparrow

高德纳箭头定义：

n↑m=nmn\uparrow m=n^{m} n↑↑m=n↑n↑……↑n↑n(mn\uparrow\uparrow m=n\uparrow n\uparrow……\uparrow n\uparrow n(m 个 )) n↑↑↑m=n↑↑n↑↑n↑↑……↑↑n↑↑n↑↑n(mn\uparrow\uparrow\uparrow m=n\uparrow\uparrow n\uparrow\uparrow n\uparrow\uparrow ……\uparrow\uparrow n\uparrow\uparrow n\uparrow\uparrow n(m 个 )) n↑gm=n↑↑↑……↑↑↑m(gn\uparrow^{g}m=n\uparrow\uparrow\uparrow……\uparrow\uparrow\uparrow m(g 个箭头 (( 注意：是箭头，不是别的，记住这个对理解葛立恒数有很大帮助))))注意：只要是用高德纳箭头表示的数，他们全都是右结合，无论多少个箭头n↑gm=n↑g−1n↑g−1……↑g−1n↑g−1n(mn\uparrow^{g}m=n\uparrow^{g-1}n\uparrow^{g-1}……\uparrow^{g-1}n\uparrow^{g-1}n(m 层 ))

接下来介绍一号男主角： GG 函数

GG 函数定义：

G(0)=4G(0)=4 G(1)=3↑43=3↑G(0)3G(1)=3\uparrow^{4}3=3\uparrow^{G(0)}3 G(2)=3↑G(1)3=3↑3↑↑↑↑33G(2)=3\uparrow^{G(1)}3=3\uparrow^{3\uparrow\uparrow\uparrow\uparrow3}3 G(n)=3↑G(n−1)3G(n)=3\uparrow^{G(n-1)}3葛立恒数 =G(64)=G(64)

你可以自己想象一下这个数有多大，抱歉，我想到一半就已经昏迷不醒了。

我可以试试用知乎自带的LaTeX写亿写葛立恒数

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WOC……好像看不清了，不过没关系。

@123问 G(G(64))G(G(64))

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（写太多卡没了）

我还没写完，不过他的层数是：

3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑3↑43333333333333333333333333333333333333333333333333333333333333333\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{3\uparrow^{4}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3}3

层（不算最顶上的那个 44 ）

其实除了高德纳箭头和葛立恒数还有很多增长率很快的符号和大数，题主可以去了解一下，由于这里是讲葛立恒数的，我就不多介绍了。

开新专栏啦！记得多投稿多支持！