一致数え上げ
from 論理と集合から始める数学の基礎 読書会
[a..b]:=[a,b]\cap\Nとした
[1..n]の順序は、自然数の順序とする
名前の意味
\le_Uの並びに反しないように\underline Uの要素と自然数とを対応付けている
\le_\bullet：\bulletの順序
つまり、\le_Uの並びに一致させて数え上げるということ
例
このHasse図で定義される順序集合に対して、\begin{array}{c|cccccc}u&1&2&3&4&5&6\\\hline \varphi(u)&a&d&b&e&c&f\end{array}で定義される\varphiは一致数え上げになる
\varphiの順に赤くなるようにした
numbering.tikz(tex)\usetikzlibrary{animations}
\begin{document}
\begin{tikzpicture}[domain=0:4]
\tikzset{
every node/.style={circle,draw,inner sep=2pt,fill=white,font=\Large},
every path/.style={very thick},
animate={
a:fill={0s="white",1s={jump,"transparent"},7s={jump,"red"},repeats},
a:draw={0s="white",1s={jump,"white"} ,7s={jump,"red"},repeats},
d:fill={0s="white",2s={jump,"transparent"},7s={jump,"red"},repeats},
d:draw={0s="white",2s={jump,"white"} ,7s={jump,"red"},repeats},
b:fill={0s="white",3s={jump,"transparent"},7s={jump,"red"},repeats},
b:draw={0s="white",3s={jump,"white"} ,7s={jump,"red"},repeats},
e:fill={0s="white",4s={jump,"transparent"},7s={jump,"red"},repeats},
e:draw={0s="white",4s={jump,"white"} ,7s={jump,"red"},repeats},
c:fill={0s="white",5s={jump,"transparent"},7s={jump,"red"},repeats},
c:draw={0s="white",5s={jump,"white"} ,7s={jump,"red"},repeats},
f:fill={0s="white",6s={jump,"transparent"},7s={jump,"red"},repeats},
f:draw={0s="white",6s={jump,"white"} ,7s={jump,"red"},repeats},
},
}
\def\s{2};
\coordinate (up) at (\s*2^-0.5,\s*2^-0.5);
\coordinate (down) at (\s*2^-0.5,\s*-2^-0.5);
\draw (0,0) node[label={right:$a$}](a){}
-- ++(up) node[label={right:$b$}](b){}
-- ++(up) node[label={right:$c$}](c){}
-- ++(down) node[label={right:$e$}](e){}
-- ++(up) node[label={right:$f$}](f){};
\draw (b)
-- ++(down) node[label={right:$d$}](d){}
-- (e);
\end{tikzpicture}
\end{document}