We establish here a few notational conventions used throughout the text.

Arithmetic with ∞

We shall sometimes use the symbols “∞” and “–∞” in simple arithmetic expressions involving real numbers. The interpretation given to such expressions is the usual, natural one; for example, for all real numbers x, we have -∞ < x < ∞, x + ∞ = ∞, x - ∞ = -∞, ∞ + ∞ = ∞, and (-∞) + (-∞) = -∞. Some such expressions have no sensible interpretation (e.g., ∞-∞).

Logarithms and exponentials

We denote by log x the natural logarithm of x. The logarithm of x to the base b is denoted logbx.

We denote by ex the usual exponential function, where e ≈ 2.71828 is the base of the natural logarithm. We may also write exp[x] instead of ex.

Sets and relations

We use the symbol ∅ to denote the empty set. For two sets A, B, we use the notation A ⊆ B to mean that A is a subset of B (with A possibly equal to B), and the notation A ⊆ B to mean that A is a proper subset of B (i.e., A ⊆ B but A ≠ B); further, A ∪ B denotes the union of A and B, A ∩ B the intersection of A and B, and A \ B the set of all elements of A that are not in B.