Elements Of Logic Via Numbers And Sets Pdf
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Elements of Logic via Numbers and Sets (Springer
It seems that you're in Germany. We have a dedicated site for Germany. In mathematics we are interested in why a particular formula is true. Intuition and statistical evidence are insufficient, so we need to construct a formal logical proof. The purpose of this book is to describe why such proofs are important, what they are made of, how to recognize valid ones, how to distinguish different kinds, and how to construct them. This book is written for 1st year students with no previous experience of formulating proofs.
Sets are well-determined collections that are completely characterized by their elements. Thus, two sets are equal if and only if they have exactly the same elements. The basic relation in set theory is that of elementhood, or membership. In particular, there is only one set with no elements at all. Of course, we can actually write down all the elements of the set when there are not too many of them. In the case of infinite sets this is clearly not possible. So, if we wish to take into account the order in which the two elements of a pair are given, we need to find another way of representing the pair.
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Elements of Logic via Numbers and Sets
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Like logic, the subject of sets is rich and interesting for its own sake. We will need only a few facts about sets and techniques for dealing with them, which we set out in this section and the next. We will return to sets as an object of study in chapters 4 and 5. A set is a collection of objects; any one of the objects in a set is called a member or an element of the set. Some sets occur so frequently that there are standard names and symbols for them.
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