Mathematical Introduction

In this section we review our basic algebraic concepts and notation. For more information, look up a basic textbook in linear algebra [1]. 1.1 Logic and sets All mathematics is based on an underlying understanding of logic. It starts of course with proposition logic, but predicate logic is the most relevant. We borrow from it its basic notation, and its basic modes of reasoning. Examples of (somewhat informal) notation: Quantor Variable ∈ Scope : Objects(V ariable) ∀x ∈ human : x will die i∈1···n : u(i) the latter abbreviated to: n i=1 u(i) Quantors are not commutative! Brackets may be used for nesting. Sets: {x[∈ Scope] : logic specification of the set of x's} Example: {x ∈ Integers : ∃y ∈ Integers(x = 2y)} specifies the set of even integers.