Fundamentals of Convex Analysis pp 1-17 | Cite as

# Introduction: Notation, Elementary Results

## Abstract

We start this chapter by listing some basic concepts, which are or should be wellknown — but it is good sometimes to return to basics. This gives us the opportunity of making precise the system of notation used in this book. For example, some readers may have forgotten that “i.e.” means *id est*, the literal translation of “that is (to say)”. If we get closer to mathematics, S∖{*x*} denotes the set obtained by depriving a set *S* function
of a point *x ∈ S*. We also mention that, if *f* is a function, *f* ^{−1} (*y*) is the *inverse image* of *y*, i.e. the set of all points *x* such that *f*(*x*) = *y*. When *f* is invertible, this set is the singleton {*f* ^{−1}(*y*)}.

## Keywords

Euclidean Space Scalar Product Orthogonal Projection Symmetric Operator Real Vector Space## Preview

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