Mathematics

Read e-book online Book of Proof PDF

By Richard Hammack

ISBN-10: 0982406207

ISBN-13: 9780982406205

This publication is an advent to the language and traditional facts tools of arithmetic. it's a bridge from the computational classes (such as calculus or differential equations) that scholars in most cases stumble upon of their first yr of faculty to a extra summary outlook. It lays a starting place for extra theoretical classes similar to topology, research and summary algebra. even though it should be extra significant to the scholar who has had a few calculus, there's relatively no prerequisite except a degree of mathematical adulthood. issues comprise units, good judgment, counting, equipment of conditional and non-conditional evidence, disproof, induction, kin, features and endless cardinality.

Show description

Read Online or Download Book of Proof PDF

Best mathematics books

Download e-book for kindle: Biomathematik: Mathematische Modelle in der Medizinischen by Reinhard Schuster

Die Phänomene in Medizin und Computational existence Sciences lassen sich in wachsendem Maße mit mathematischen Modellen beschreiben. In diesem Buch werden Mechanismen der Modellbildung beginnend von einfachen Ansätzen (z. B. exponentielles Wachstum) bis zu Elementen moderner Theorien, wie z. B. unterschiedliche Zeitskalen in der Michaelis-Menten-Theorie in der Enzymkinetik, vorgestellt.

Extra info for Book of Proof

Example text

Every universally quantified statement can be expressed as a conditional statement. 2 Suppose S is a set and Q ( x) is a statement about x for each x ∈ S . The following statements mean the same thing. ∀ x ∈ S, Q ( x) ( x ∈ S ) ⇒ Q ( x) Translating English to Symbolic Logic 51 This fact is significant because so many theorems have the form of a conditional statement. ) In proving a theorem we have to think carefully about what it says. Sometimes a theorem will be expressed as a universally quantified statement but it will be more convenient to think of it as a conditional statement.

P : If an integer x is a multiple of 6, then x is even. This is a sentence that is true. ) Since the sentence P is definitely true, it is a statement. When a sentence or statement P contains a variable such as x, we sometimes denote it as P ( x) to indicate that it is saying something about x. Thus the above statement can be expressed as P ( x) : If an integer x is a multiple of 6, then x is even. A statement or sentence involving two variables might be denoted P ( x, y), and so on. It is quite possible for a sentence containing variables to not be a statement.

4 4 (a) (b) Ai = i =1 Ai = i =1   A1 A 2. Suppose  2 A3 = = = 0, 2, 4, 8, 10, 12, 14, 16, 18, 20, 22, 24 , 0, 3, 6, 9, 12, 15, 18, 21, 24 , 0, 4, 8, 12, 16, 20, 24 . 3 3 (a) (b) Ai = i =1 Ai = i =1 3. For each n ∈ N, let A n = 0, 1, 2, 3, . . , n . (a) (b) Ai = i ∈N Ai = i ∈N 4. For each n ∈ N, let A n = − 2n, 0, 2n . (a) (b) Ai = i ∈N 5. (a) (b) [ i, i + 1] = i ∈N 6. (a) (b) [0, i + 1] = R × [ i, i + 1] = 8. (a) α∈R α × [0, 1] = 10. (a) (b) α∈R X= (b) [ x, 1] × [0, x2 ] = (b) X ∈P (N) α∈ I X= [ x, 1] × [0, x2 ] = x∈[0,1] Aα ⊆ Aα = α × [0, 1] = X ∈P (N) x∈[0,1] 12.

Download PDF sample

Book of Proof by Richard Hammack


by David
4.3

Rated 4.98 of 5 – based on 36 votes