3.5 Paradox ☆1. Russells paradox 令A∈A,AgA。 o Russells paradox: Let SAAsA. The question is, does s∈S sie.S∈ Sor SEs? IsEs, 冷IfS∈S, ☆ The statements"S∈s"and"SgS" cannot both be true. thus the contradiction
3.5 Paradox ❖ 1.Russell’s paradox ❖ AA, AA。 ❖ Russell’s paradox: Let S={A|AA}. The question is, does SS? ❖ i.e. SS or SS? ❖ If SS, ❖ If SS, ❖ The statements " SS " and " SS " cannot both be true, thus the contradiction
☆2. Cantor, s paradox 81899, Cantor's paradox, sometimes called the paradox of the greatest cardinal expresses what its second name would imply--that there is no cardinal larger than every other cardinal 冷 Let s be the set of all sets..S?≤|P(S)or P(S)?≤(S .g The third crisis in mathematics
❖ 2.Cantor’s paradox ❖ 1899,Cantor's paradox, sometimes called the paradox of the greatest cardinal, expresses what its second name would imply--that there is no cardinal larger than every other cardinal. ❖ Let S be the set of all sets. |S|?|P (S)| or |P (S)|?|(S)| ❖ The Third Crisis in Mathematics
II Introductory Combinatorics Chapter 4 Introductory Combinatorics Counting
II Introductory Combinatorics Chapter 4 Introductory Combinatorics Counting
Combinatorics, is an important part of discrete mathematics Techniques for counting are important in computer science, especially in the analysis of algorithm. ☆ sorting, searching g combinatorial algorithms . Combinatorics
❖ Combinatorics, is an important part of discrete mathematics. ❖ Techniques for counting are important in computer science, especially in the analysis of algorithm. ❖ sorting,searching ❖ combinatorial algorithms ❖ Combinatorics
☆ existence counting 今 construction ☆ optimization 4 existence Pigeonhole principle .& o Counting techniques for permutation and combinations, and Generating function, and Recurrence relations
❖ existence ❖ counting ❖ construction ❖ optimization ❖ existence :Pigeonhole principle ❖ Counting techniques for permutation and combinations,and Generating function, and Recurrence relations