等式可證,該圖的交叉數必多於直線的二元組數,但此為不可能(因為兩條直線只能交於獨一點)。此不等式同樣適用於證明貝克定理(英语:Beck'stheorem (geometry)),即若平面上 n {\displaystyle n} 個點中,不存在線性多(即 n / C {\displaystyle n/C}
Commentary on The Emperor's New Mind. Behavioral and Brain Sciences 13 (4) 655. Davis, Martin 1993. How subtle is Gödel'stheorem? More on Roger Penrose