epdf.pub_the-nuts-and-bolts-of-proofs-third-edition-an-intr

178 Index
If/Then statements
direct proof, 12-19
negation construction, 25-30
overview, 9-12
proof by contrapositive, 22-25
related statements, 19-22
Indirect proof, see Proof by
contrapositive
Induction (Mathematical), 48-57
Intersection of sets, 71
Inverse of a statement, 20
L
Lemma, 3-4
Limits, 92-101
Logical equivalence, 19-20
M
Mathematical induction, 48-57
Multiple conclusions, 84
Multiple hypotheses, 82-84
N
Necessary condition, 10
Negation of a statement, 25-30
o
One-to-one function, 19
Palindrome number, 31
Principle of Mathematical
Induction
definition, 49
strong, 52-53
weak, 52-53
Proof by contradiction, 22-25,
28-29
Proof by contrapositive, 22-25,
28-29
Proof concepts, 3, 5-8
Q
Quantifiers, 25
R
Related statements, 19-22
Roster method, 68
Sequence, 99
Sets
complement, 74
definition, 68
element, 68
empty, 68
equahty, 68-76
intersection, 71
universal, 69
Simple statement, 2
Sound proof, 8
Statements
composite, 2, 26, 81-90
contrapositive, 20
converse, 20
If/Then statements, 9-30
inverse, 20
negation, 25-30
related, 19-22
simple, 2
Strong principle of mathematical
induction, 52-53
Sufficient condition, 10