ATFL - Lecture #2
Mathematical Preliminaries
1
, Mathematical Preliminaries
• Sets
• Functions
• Relations
• Graphs
• Proof Techniques
2
, SETS
A set is a collection of elements
A {1, 2, 3}
B {train, bus, bicycle, airplane}
We write
1 A
ship B
3
, Set Representations
C = { a, b, c, d, e, f, g, h, i, j, k }
C = { a, b, …, k } finite set
S = { 2, 4, 6, … } infinite set
S = { j : j > 0, and j = 2k for some k>0 }
S = { j : j is nonnegative and even }
4
Mathematical Preliminaries
1
, Mathematical Preliminaries
• Sets
• Functions
• Relations
• Graphs
• Proof Techniques
2
, SETS
A set is a collection of elements
A {1, 2, 3}
B {train, bus, bicycle, airplane}
We write
1 A
ship B
3
, Set Representations
C = { a, b, c, d, e, f, g, h, i, j, k }
C = { a, b, …, k } finite set
S = { 2, 4, 6, … } infinite set
S = { j : j > 0, and j = 2k for some k>0 }
S = { j : j is nonnegative and even }
4
