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# Some Preliminaries

DOI link for Some Preliminaries

Some Preliminaries book

# Some Preliminaries

DOI link for Some Preliminaries

Some Preliminaries book

## ABSTRACT

This chapter reviews some of the ideas and notation from set theory and discusses the notion of a function. Mathematics is distinguished from all other sciences by its insistence on rigor: every statement must be derived by logical rules from clearly stated assumptions. There is often a need in mathematics to say that two things are equivalent to each other in some sense. For instance, congruent triangles can be regarded as the same for most purposes in geometry; for some purposes, when size is unimportant, similar triangles can be regarded as equivalent. Mathematicians have therefore found it useful to systematize the notion of equivalence. Mathematical induction is a somewhat specialized, but very useful, method of proof. In principle, every mathematical statement which is not an axiom or a definition should be proved.