Discrete mathematics Yi Li Software school Fudan universit March 12. 2013
. . Discrete Mathematics Yi Li Software School Fudan University March 12, 2013 Yi Li (Fudan University) Discrete Mathematics March 12, 2013 1 / 20
Review of lattice Special Lattice Boolean algebra
Review of Lattice Ideal Special Lattice Boolean Algebra Yi Li (Fudan University) Discrete Mathematics March 12, 2013 2 / 20
Examples of Proof Zenos paradox Zhuang Zi's paradox o Gong Sunlong's"a white horse is not a horse How can you persuade yourself and the others?
Examples of Proof Zeno’s paradox Zhuang Zi’s paradox Gong Sunlong’s “a white horse is not a horse” ... How can you persuade yourself and the others? Yi Li (Fudan University) Discrete Mathematics March 12, 2013 3 / 20
Examples of Proof A×iom The axiom of group theory can be formulated as follows (G1) For all 9, 2: (aoy)ox=ao(yo z G2)Fora∥:xoe=x (G3)For every there is a y such that r y=e.(right Inverse Theorem For every a there is a y such that yo =e. left inverse
Examples of Proof . Axiom . . The axiom of group theory can be formulated as follows: (G1) For all x, y, z: (x ◦ y) ◦ z = x ◦ (y ◦ z). (G2) For all x: x ◦ e = x. (G3) For every x there is a y such that x ◦ y = e. (right inverse) . Theorem . . For every x there is a y such that y ◦ x = e.(left inverse) Yi Li (Fudan University) Discrete Mathematics March 12, 2013 4 / 20
What is LogIc o Premise Argument o Conclusion o Follow o Proof
What is Logic Premise Argument Conclusion Follow Proof Yi Li (Fudan University) Discrete Mathematics March 12, 2013 5 / 20