The primary purpose of this undergraduate text is to teach students to do mathematical proofs. It enables readers to recognize the elements that constitute an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. The self-contained treatment features many exercises, problems, and selected answers, including worked-out solutions. Starting with sets and rules of inference, this text covers functions, relations, operation, and the integers. Additional topics include proofs in analysis, cardinality, and groups. Six appendixes offer supplemental material. Teachers will welcome the return of this long-out-of-print volume, appropriate for both one- and two-semester courses.
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Yes, you can access Introduction to Proof in Abstract Mathematics by Andrew Wohlgemuth in PDF and/or ePUB format, as well as other popular books in Mathematics & Logic in Mathematics. We have over one million books available in our catalogue for you to explore.
We begin this section with a review of some notation and informal ideas about sets now common in the school curriculum. A set is a collection of things viewed as a whole. The things in a set are called elements or members of the set. The expression “x
A” means that x is a member of set A and is read “x is an element of A” or “x is a member of A”. The expression “x ∉ A” means that x is not a member of A. We will assume that all sets are formed of elements from some universal set
under consideration. The set of real numbers will be denoted by
, integers by
, and positive integers by
.
We will not give a formal definition of set. It will be an undefined term—a starting point in terms of which we will define other things. While the idea of a set is undefined, we will assume that any particular set may be defined by giving a rule for deciding which elements of the universal set are in the particular set and which are not.
For example, if
is our universal set, then the set of all real numbers between 0 and 1 is written {x
| 0 < x < 1}. This is read “the set of all x in
such that zero is less than x and x is less than one”. In the expression “{x
| 0 < x < 1}”, the symbol “x” is used as a local v...
