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December 7, 2018 07:10
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dependency graph of theorems in real analysis
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\begin{tikzpicture} | |
\node[draw,text width=3.5cm] (lub) at (5,10) {Least upper bound property}; | |
\node[draw,text width=4cm] (bw) at (0,0) {Bolzano--Weierstrass theorem}; | |
\node[draw,text width=3cm] (nested) at (11,0) {Nested intervals theorem}; | |
\node[draw,text width=3cm] (ivt) at (11,5) {Intermediate value theorem}; | |
\node[draw,text width=3cm] (bounded) at (5,5) {Boundedness theorem}; | |
\node[draw,text width=3cm] (evt) at (0,5) {Extreme value theorem}; | |
\draw[->] (lub) -- (nested) node[midway, fill=white, text width=1.5cm] {Stillwell, Folland}; | |
\draw[->] (lub) -- (evt) node[midway, fill=white] {Spivak}; | |
\draw[->] (lub) -- (bounded) node[midway, fill=white] {Spivak}; | |
\draw[->] (lub) -- (ivt) node[midway, fill=white] {Spivak}; | |
\draw[->] (nested) -- (ivt) node[midway, fill=white] {Stillwell}; | |
\draw[->] (bw) -- (ivt) node[midway, fill=white] {Tao}; | |
\draw[->] (bw) -- (bounded) node[midway, fill=white, text width=1.5cm] {Tao, Folland}; | |
\draw[->] (bw) -- (evt) node[midway, fill=white, text width=1.5cm] {Tao, Folland}; | |
\draw[->] (lub) -- (bw) node[midway, fill=white] {Tao}; | |
\draw[->] (nested) -- (bw) node[midway, fill=white, text width=1.5cm] {Stillwell, Folland}; | |
\end{tikzpicture} |
Author
riceissa
commented
Dec 7, 2018
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