Large Number Lying on the Boundary of the Rule of Touhou Large Number 4

Large Number Lying on the Boundary of the Rule of Touhou Large Number 4 (Japanese: 東方巨大数4の規則の境界を突いた巨大数) is a large number submitted to a Japanese large number contest.東方巨大数4の規則の境界を突いた巨大数 The term was coined by 巨大数大好きbot on 28/07/2021.
==八雲語==
巨大数大好きbot invented 八雲語, which is a mathematical language similar to an assembly language, to describe the definition. Let \(K\) denote the set of alphabets given as 常用漢字, i.e. kanjis in Japanese standard level, and \(F\) denote the set of all maps of type \(K \to (\mathbb{Z}^2 \to \mathbb{Z})\). 八雲語 is formulated so that each sentence describes a map of type \(F \to F\).
Although 八雲語 is a language imitating an assembly languageMore precisely, since the language admits controlling structures like an if-sentence and a for-loop, it is rather close to C language., it is formulated as a partial map from the set \(S\) of formal strings consisting of one or more Unicode letters to the set of all maps of type \(F \to F\).
Roughly speaking, elements of \(K\) correspond to a name of a variable for a two dimensional array, elements of \(F\) correspond to data in the memory, elements of \(S\) correspond to formal strings expressing commands, and "partial maps from \(S\) to the set of all maps of type \(F \to F\)" correspond to sets of commands.
==Definition==
Let \(z \in F\) denote the lambda expression λk. (λx,y. 0), and define 東方巨大数4の規則の境界を突いた巨大数 as the resulting value of the estimation of the following function written in 八雲語:
繝ﾘ龍繝ﾝ繝ｾ底繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ繧ｮ繝ﾝ縺ｽ縺ｫ繧ｮ縺ｪ哀縺ｬ繝ｾ龍繝ｧ哀繧ｧ繝ｯ繧ｧ繝ｦ繝ｨ哀繧ｧ繝ｯ繧ｧ繝ｦ繝ｫ哀繧ｧ繝ｯ繧ｧ繝ｦ繝ﾝ縺ﾝ繝ｾ高繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ繧ｮ繝ﾝ繝ｾ切繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ繧ｮ繝ﾝ繝ｾ切繝ｧ繧ｧ繝ｨ繧ｨ繝ｫ繧ｮ繝ﾝ縺ｶ切縺ｧ繧ｧ縺ｨ繧ｧ縺ｫ繧ｨ縺ｬ縺ﾅ切縺ｧ繧ｧ縺ｨ繧ｨ縺ｫ繧ｨ縺ｬ繝ｾ龍繝ｧ切繧ｧ繝ｯ繧ｧ繝ｦ繝ｨ切繧ｧ繝ｯ繧ｨ繝ｦ繝ｫ繧ｧ繝ﾝ繝ｲ切繝ｧ繧ｧ繝ｨ繧ｨ繝ｫ繧ｦ繧ｨ繝ﾝ繝ｾ典繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ龍切繧ｧ繝ｯ繧ｧ繝ｦ繝ｯ切繧ｧ繝ｯ繧ｨ繝ｦ繝ｦ繝ﾝ縺ﾗ典縺ｧ繧ｧ縺ｨ繧ｧ縺ｫ繧ｧ縺ｬ繝ｲ切繝ｧ繧ｧ繝ｨ繧ｨ繝ｫ繧ｨ繝ﾝ繝ｾ典繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ龍切繧ｧ繝ｯ繧ｧ繝ｦ繝ｯ切繧ｧ繝ｯ繧ｨ繝ｦ繝ｦ繝ﾝ縺ﾝ繝ｲ底繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ繧ｨ繝ﾝ縺ｭ繝ｾ悪繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ切繧ｧ繝ｯ繧ｧ繝ｦ繝ﾝ繝ｾ悪繝ｧ繧ｧ繝ｨ繧ｨ繝ｫ切繧ｧ繝ｯ繧ｨ繝ｦ繝ﾝ繝ｾ差繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ繧ｧ繝ﾝ縺ｲ差縺ｧ繧ｧ縺ｨ繧ｧ縺ｫ繧ｧ縺ｬ繝ｲ悪繝ｧ繧ｧ繝ｨ繧ｨ繝ｫ繧ｦ繧ｨ繝ﾝ繝ｾ根繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ繧ｧ繝ﾝ縺ﾗ根縺ｧ繧ｧ縺ｨ繧ｧ縺ｫ繧ｧ縺ｬ繝ｲ悪繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ繧ｦ繧ｨ繝ﾝ繝ｾ根繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ龍悪繧ｧ繝ｯ繧ｧ繝ｦ繝ｯ悪繧ｧ繝ｯ繧ｨ繝ｦ繝ｦ繝ﾝ縺ﾝ繝ｻ差繝ｧ繧ｧ繝ｨ繧ｧ繝ﾎ龍繝ｧ悪繧ｧ繝ｯ繧ｧ繝ｦ繝ｨ悪繧ｧ繝ｯ繧ｨ繝ｦ繝ﾎ根繝ｧ繧ｧ繝ｨ繧ｧ繝ﾝ縺ﾝ繝ｻ移繝ｧ繧ｧ繝ｨ繧ｧ繝ﾎ切繝ｧ繧ｧ繝ｨ繧ｧ繝ﾎ悪繝ｧ繧ｧ繝ｨ繧ｧ繝ﾝ繝ｻ移繝ｧ繧ｧ繝ｨ繧ｨ繝ﾎ切繝ｧ繧ｧ繝ｨ繧ｨ繝ﾎ悪繝ｧ繧ｧ繝ｨ繧ｨ繝ﾝ縺ﾀ差縺ｧ繧ｧ縺ｨ繧ｧ縺ｫ繧ｧ縺ｬ繝ｲ移繝ｧ繧ｧ繝ｨ繧ｨ繝ｫ繧ｦ繧ｨ繝ﾝ縺ﾝ繝ｻ写繝ｧ繧ｧ繝ｨ繧ｨ繝ﾎ高繝ｧ繧ｧ繝ｨ繧ｧ繝ﾎ悪繝ｧ繧ｧ繝ｨ繧ｨ繝ﾝ繝ｾ昇繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ繧ｧ繝ﾝ繝ｱ向繝ｧ繧ｧ繝ｨ繧ｧ繝ﾎ悪繝ｧ繧ｧ繝ｨ繧ｧ繝ﾎ移繝ｧ繧ｧ繝ｨ繧ｧ繝ﾝ縺ｻ縺ｫ底繧ｧ繝ｯ繧ｧ繝ｦ縺ｬ縺ｻ縺ｫ移繧ｧ繝ｯ繧ｧ繝ｦ縺ｬ繝ｻ泉繝ｧ繧ｧ繝ｨ繧ｧ繝ﾎ向繝ｧ繧ｧ繝ｨ繧ｧ繝ﾎ移繝ｧ繧ｧ繝ｨ繧ｧ繝ﾝ繝ｱ向繝ｧ繧ｧ繝ｨ繧ｨ繝ﾎ悪繝ｧ繧ｧ繝ｨ繧ｨ繝ﾎ移繝ｧ繧ｧ繝ｨ繧ｨ繝ﾝ繝ｱ向繝ｧ繧ｧ繝ｨ繧ｨ繝ﾎ向繝ｧ繧ｧ繝ｨ繧ｨ繝ﾎ昇繝ｧ繧ｧ繝ｨ繧ｧ繝ﾝ縺ｻ縺ｫ写繧ｧ繝ｯ繧ｨ繝ｦ縺ｬ繝ｻ泉繝ｧ繧ｧ繝ｨ繧ｨ繝ﾎ向繝ｧ繧ｧ繝ｨ繧ｨ繝ﾎ移繝ｧ繧ｧ繝ｨ繧ｨ繝ﾝ繝ｺ龍繝ｧ向繧ｧ繝ｯ繧ｧ繝ｦ繝ｨ向繧ｧ繝ｯ繧ｨ繝ｦ繝ﾎ龍繝ｧ泉繧ｧ繝ｯ繧ｧ繝ｦ繝ｨ泉繧ｧ繝ｯ繧ｨ繝ｦ繝ﾝ繝ｲ向繝ｧ繧ｧ繝ｨ繧ｨ繝ｫ繧ｨ繝ﾝ縺ﾝ繝ｲ向繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ繧ｨ繝ﾝ繝ｲ切繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ繧ｨ繝ﾝ縺ﾝ繝ｱ高繝ｧ繧ｧ繝ｨ繧ｧ繝ﾎ高繝ｧ繧ｧ繝ｨ繧ｧ繝ﾎ移繝ｧ繧ｧ繝ｨ繧ｨ繝ﾝ繝ｱ昇繝ｧ繧ｧ繝ｨ繧ｧ繝ﾎ昇繝ｧ繧ｧ繝ｨ繧ｧ繝ﾎ移繝ｧ繧ｧ繝ｨ繧ｨ繝ﾝ縺ﾝ繝ｲ切繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ繧ｦ繧ｨ繝ﾝ繝ｾ切繝ｧ繧ｧ繝ｨ繧ｨ繝ｫ繧ｧ繝ﾝ繝ｾ典繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ龍切繧ｧ繝ｯ繧ｧ繝ｦ繝ｯ切繧ｧ繝ｯ繧ｨ繝ｦ繝ｦ繝ﾝ縺ﾗ典縺ｧ繧ｧ縺ｨ繧ｧ縺ｫ繧ｧ縺ｬ繝ｲ切繝ｧ繧ｧ繝ｨ繧ｨ繝ｫ繧ｨ繝ﾝ繝ｾ典繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ龍切繧ｧ繝ｯ繧ｧ繝ｦ繝ｯ切繧ｧ繝ｯ繧ｨ繝ｦ繝ｦ繝ﾝ縺ﾝ繝ｲ底繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ繧ｨ繝ﾝ縺ﾝ縺ﾝ繝ｾ龍繝ｧ切繧ｧ繝ｯ繧ｧ繝ｦ繝ｨ切繧ｧ繝ｯ繧ｨ繝ｦ繝ｫ繧ｧ繝ﾝ繝ｲ底繝ｧ繝ｨ繧ｧ繝ｫ繧ｧ繝ﾝ(z)(底)(0,0)
===Refactoring===
Since the original definition above is difficult to read, the creator wrote a code inserting new lines, blank lines, and indents to it so that it becomes easier to read (except for the portion (z)(底)(0,0)) right after the description of it.
繝ﾘ龍繝ﾝ
繝ｾ底繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ繧ｮ繝ﾝ
縺ｽ縺ｫ繧ｮ縺ｪ哀縺ｬ
    繝ｾ龍繝ｧ哀繧ｧ繝ｯ繧ｧ繝ｦ繝ｨ哀繧ｧ繝ｯ繧ｧ繝ｦ繝ｫ哀繧ｧ繝ｯ繧ｧ繝ｦ繝ﾝ
縺ﾝ
繝ｾ高繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ繧ｮ繝ﾝ
繝ｾ切繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ繧ｮ繝ﾝ
繝ｾ切繝ｧ繧ｧ繝ｨ繧ｨ繝ｫ繧ｮ繝ﾝ
縺ｶ切縺ｧ繧ｧ縺ｨ繧ｧ縺ｫ繧ｨ縺ｬ
    縺ﾅ切縺ｧ繧ｧ縺ｨ繧ｨ縺ｫ繧ｨ縺ｬ
       繝ｾ龍繝ｧ切繧ｧ繝ｯ繧ｧ繝ｦ繝ｨ切繧ｧ繝ｯ繧ｨ繝ｦ繝ｫ繧ｧ繝ﾝ
       繝ｲ切繝ｧ繧ｧ繝ｨ繧ｨ繝ｫ繧ｦ繧ｨ繝ﾝ
       繝ｾ典繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ龍切繧ｧ繝ｯ繧ｧ繝ｦ繝ｯ切繧ｧ繝ｯ繧ｨ繝ｦ繝ｦ繝ﾝ
       縺ﾗ典縺ｧ繧ｧ縺ｨ繧ｧ縺ｫ繧ｧ縺ｬ
           繝ｲ切繝ｧ繧ｧ繝ｨ繧ｨ繝ｫ繧ｨ繝ﾝ
           繝ｾ典繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ龍切繧ｧ繝ｯ繧ｧ繝ｦ繝ｯ切繧ｧ繝ｯ繧ｨ繝ｦ繝ｦ繝ﾝ
       縺ﾝ
       繝ｲ底繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ繧ｨ繝ﾝ
    縺ｭ
       繝ｾ悪繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ切繧ｧ繝ｯ繧ｧ繝ｦ繝ﾝ
       繝ｾ悪繝ｧ繧ｧ繝ｨ繧ｨ繝ｫ切繧ｧ繝ｯ繧ｨ繝ｦ繝ﾝ
       繝ｾ差繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ繧ｧ繝ﾝ
       縺ｲ差縺ｧ繧ｧ縺ｨ繧ｧ縺ｫ繧ｧ縺ｬ
           繝ｲ悪繝ｧ繧ｧ繝ｨ繧ｨ繝ｫ繧ｦ繧ｨ繝ﾝ
           繝ｾ根繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ繧ｧ繝ﾝ
           縺ﾗ根縺ｧ繧ｧ縺ｨ繧ｧ縺ｫ繧ｧ縺ｬ
               繝ｲ悪繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ繧ｦ繧ｨ繝ﾝ
               繝ｾ根繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ龍悪繧ｧ繝ｯ繧ｧ繝ｦ繝ｯ悪繧ｧ繝ｯ繧ｨ繝ｦ繝ｦ繝ﾝ
           縺ﾝ
           繝ｻ差繝ｧ繧ｧ繝ｨ繧ｧ繝ﾎ龍繝ｧ悪繧ｧ繝ｯ繧ｧ繝ｦ繝ｨ悪繧ｧ繝ｯ繧ｨ繝ｦ繝ﾎ根繝ｧ繧ｧ繝ｨ繧ｧ繝ﾝ
       縺ﾝ
       繝ｻ移繝ｧ繧ｧ繝ｨ繧ｧ繝ﾎ切繝ｧ繧ｧ繝ｨ繧ｧ繝ﾎ悪繝ｧ繧ｧ繝ｨ繧ｧ繝ﾝ
       繝ｻ移繝ｧ繧ｧ繝ｨ繧ｨ繝ﾎ切繝ｧ繧ｧ繝ｨ繧ｨ繝ﾎ悪繝ｧ繧ｧ繝ｨ繧ｨ繝ﾝ
       縺ﾀ差縺ｧ繧ｧ縺ｨ繧ｧ縺ｫ繧ｧ縺ｬ
           繝ｲ移繝ｧ繧ｧ繝ｨ繧ｨ繝ｫ繧ｦ繧ｨ繝ﾝ
       縺ﾝ
       繝ｻ写繝ｧ繧ｧ繝ｨ繧ｨ繝ﾎ高繝ｧ繧ｧ繝ｨ繧ｧ繝ﾎ悪繝ｧ繧ｧ繝ｨ繧ｨ繝ﾝ
       繝ｾ昇繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ繧ｧ繝ﾝ
       繝ｱ向繝ｧ繧ｧ繝ｨ繧ｧ繝ﾎ悪繝ｧ繧ｧ繝ｨ繧ｧ繝ﾎ移繝ｧ繧ｧ繝ｨ繧ｧ繝ﾝ
       縺ｻ縺ｫ底繧ｧ繝ｯ繧ｧ繝ｦ縺ｬ
           縺ｻ縺ｫ移繧ｧ繝ｯ繧ｧ繝ｦ縺ｬ
               繝ｻ泉繝ｧ繧ｧ繝ｨ繧ｧ繝ﾎ向繝ｧ繧ｧ繝ｨ繧ｧ繝ﾎ移繝ｧ繧ｧ繝ｨ繧ｧ繝ﾝ
               繝ｱ向繝ｧ繧ｧ繝ｨ繧ｨ繝ﾎ悪繝ｧ繧ｧ繝ｨ繧ｨ繝ﾎ移繝ｧ繧ｧ繝ｨ繧ｨ繝ﾝ
               繝ｱ向繝ｧ繧ｧ繝ｨ繧ｨ繝ﾎ向繝ｧ繧ｧ繝ｨ繧ｨ繝ﾎ昇繝ｧ繧ｧ繝ｨ繧ｧ繝ﾝ
               縺ｻ縺ｫ写繧ｧ繝ｯ繧ｨ繝ｦ縺ｬ
                   繝ｻ泉繝ｧ繧ｧ繝ｨ繧ｨ繝ﾎ向繝ｧ繧ｧ繝ｨ繧ｨ繝ﾎ移繝ｧ繧ｧ繝ｨ繧ｨ繝ﾝ
                   繝ｺ龍繝ｧ向繧ｧ繝ｯ繧ｧ繝ｦ繝ｨ向繧ｧ繝ｯ繧ｨ繝ｦ繝ﾎ龍繝ｧ泉繧ｧ繝ｯ繧ｧ繝ｦ繝ｨ泉繧ｧ繝ｯ繧ｨ繝ｦ繝ﾝ
                   繝ｲ向繝ｧ繧ｧ繝ｨ繧ｨ繝ｫ繧ｨ繝ﾝ
               縺ﾝ
               繝ｲ向繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ繧ｨ繝ﾝ
               繝ｲ切繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ繧ｨ繝ﾝ
           縺ﾝ
           繝ｱ高繝ｧ繧ｧ繝ｨ繧ｧ繝ﾎ高繝ｧ繧ｧ繝ｨ繧ｧ繝ﾎ移繝ｧ繧ｧ繝ｨ繧ｨ繝ﾝ
           繝ｱ昇繝ｧ繧ｧ繝ｨ繧ｧ繝ﾎ昇繝ｧ繧ｧ繝ｨ繧ｧ繝ﾎ移繝ｧ繧ｧ繝ｨ繧ｨ繝ﾝ
       縺ﾝ
       繝ｲ切繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ繧ｦ繧ｨ繝ﾝ
       繝ｾ切繝ｧ繧ｧ繝ｨ繧ｨ繝ｫ繧ｧ繝ﾝ
       繝ｾ典繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ龍切繧ｧ繝ｯ繧ｧ繝ｦ繝ｯ切繧ｧ繝ｯ繧ｨ繝ｦ繝ｦ繝ﾝ
       縺ﾗ典縺ｧ繧ｧ縺ｨ繧ｧ縺ｫ繧ｧ縺ｬ
           繝ｲ切繝ｧ繧ｧ繝ｨ繧ｨ繝ｫ繧ｨ繝ﾝ
           繝ｾ典繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ龍切繧ｧ繝ｯ繧ｧ繝ｦ繝ｯ切繧ｧ繝ｯ繧ｨ繝ｦ繝ｦ繝ﾝ
       縺ﾝ
       繝ｲ底繝ｧ繧ｧ繝ｨ繧ｧ繝ｫ繧ｨ繝ﾝ
    縺ﾝ
縺ﾝ
繝ｾ龍繝ｧ切繧ｧ繝ｯ繧ｧ繝ｦ繝ｨ切繧ｧ繝ｯ繧ｨ繝ｦ繝ｫ繧ｧ繝ﾝ
繝ｲ底繝ｧ繝ｨ繧ｧ繝ｫ繧ｧ繝ﾝ
==Footnotes==
==Sources==
==See also==
ja:東方巨大数4の規則の境界を突いた巨大数
Category:Numbers
Category:Googology in Asia