Discrete mathematics Yi Li Software school Fudan universit March 13. 2012
Discrete Mathematics Yi Li Software School Fudan University March 13, 2012 Yi Li (Fudan University) Discrete Mathematics March 13, 2012 1 / 20
Review of lattice o Special Lattice ● Boolean Algebra
Review of Lattice Ideal Special Lattice Boolean Algebra Yi Li (Fudan University) Discrete Mathematics March 13, 2012 2 / 20
Examples of Proof Zenos paradox o Zhuang Zis 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 13, 2012 3 / 20
Examples of Proof A×iom The axiom of group theory can be formulated as follows (G1) For all 9, z:(aoy)ox=xo(yo 2) G2)Fora∥x:xoe=x (G3) For every there is a y such that coy =e Theorem For every c there is a y such that yo =e
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. Theorem For every x there is a y such that y ◦ x = e. Yi Li (Fudan University) Discrete Mathematics March 13, 2012 4 / 20
What is LogIc Premise Argument o Conclusion o Follow o Proof
What is Logic Premise Argument Conclusion Follow Proof Yi Li (Fudan University) Discrete Mathematics March 13, 2012 5 / 20