Testing Math Markup

[hollyking]

By an Interval we mean a closed bounded set of “real” numbers

[a, b] = { x : a ≤ x ≤ b }.

We can also regard an interval as a number represented by the ordered pair of its enpoints a and b; just as we represent a rational number, a⁄b, by an ordered pair of integers. Thus, intervals have a dual nature, as we shall see, representing a set of real numbers by a new kind of number.

Intervals are denoted by capital letters. Furthurmore if X is an interval, its endpoints are denoted by X and X. Thus, X = [X, X].

An n-dimensional interval vector is an ordered n-tuple of intervals (X₁, X₂, · · ·, X_n). Interval vectors are also denoted by capital letters. If X is a two-dimensional interval vector, then X = (X₁, X₂), so X₁ = [X₁, X₁] and X₂ = [X₂, X₂]. Math::Interval does not distinguish between the degenerate interval [a, a] and the real number, a.