Course MA2C01, Michaelmas Term 2012 Section 2: Sets and Functions
نویسنده
چکیده
2 Sets and Functions 10 2.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Unions, Intersections and Complements of Sets . . . . . . . . . 10 2.3 Subsets and Power Sets . . . . . . . . . . . . . . . . . . . . . . 12 2.4 The Specification of Sets . . . . . . . . . . . . . . . . . . . . . 14 2.5 Binary Relations . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.6 Congruences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.7 Partitions and Equivalence Relations . . . . . . . . . . . . . . 18 2.8 Partial Orders and Lattices . . . . . . . . . . . . . . . . . . . 19 2.9 Cartesian Products of Sets . . . . . . . . . . . . . . . . . . . . 20 2.10 Functions between Sets . . . . . . . . . . . . . . . . . . . . . . 22 2.11 Compositions of Functions . . . . . . . . . . . . . . . . . . . . 23 2.12 The Graph of a Function . . . . . . . . . . . . . . . . . . . . . 23 2.13 The Inverse of a Function . . . . . . . . . . . . . . . . . . . . 24 2.14 Injective, Surjective and Bijective Functions . . . . . . . . . . 25 2.15 Functions defined on Finite Sets . . . . . . . . . . . . . . . . . 28
منابع مشابه
Course MA2C01, Michaelmas Term 2012 Section 3: Abstract Algebra
3 Abstract Algebra 32 3.1 Binary Operations on Sets . . . . . . . . . . . . . . . . . . . . 32 3.2 Commutative Binary Operations . . . . . . . . . . . . . . . . 32 3.3 Associative Binary Operations . . . . . . . . . . . . . . . . . . 32 3.4 Semigroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.5 The General Associative Law . . . . . . . . . . . . . . . . . . 34 3.6 Identity el...
متن کاملCourse 221: Michaelmas Term 2006 Section 1: Sets, Functions and Countability
1 Sets, Functions and Countability 2 1.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Cartesian Products of Sets . . . . . . . . . . . . . . . . . . . . 5 1.3 Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Equivalence Relations . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Functions . . . . . . . . . . . . . . . . . . . . . . . . ...
متن کاملCourse 2BA1: Michaelmas Term 2005 Section 2: Sets and Functions
2 Sets and Functions 1 2.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2.2 Unions, Intersections and Complements of Sets . . . . . . . . . 2 2.3 Subsets and Power Sets . . . . . . . . . . . . . . . . . . . . . . 4 2.4 The Specification of Sets . . . . . . . . . . . . . . . . . . . . . 6 2.5 Binary Relations . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.6 Congr...
متن کاملCourse 2BA1: Michaelmas Term 2006 Section 5: Sets and Functions
5 Sets and Functions 1 5.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5.2 Unions, Intersections and Complements of Sets . . . . . . . . . 2 5.3 Subsets and Power Sets . . . . . . . . . . . . . . . . . . . . . . 4 5.4 The Specification of Sets . . . . . . . . . . . . . . . . . . . . . 6 5.5 Binary Relations . . . . . . . . . . . . . . . . . . . . . . . . . 7 5.6 Congr...
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2 Sets and Functions 10 2.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Unions, Intersections and Complements of Sets . . . . . . . . . 10 2.3 Subsets and Power Sets . . . . . . . . . . . . . . . . . . . . . . 12 2.4 The Specification of Sets . . . . . . . . . . . . . . . . . . . . . 14 2.5 Binary Relations . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.6...
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