Mathematical Conventions

When using mathematical notation in this reference document, the following conventions are observed:

• A sequence \(s = (x_0, x_1, \ldots, x_k)\) uses zero-based indexing: \(s(i) = x_i\).

• An empty product (a product over a sequence of length zero) is understood to have value \(1\).

• An empty sum (a sum over a sequence of length zero) is understood to have value \(0\).

• A computation described using mathematical notation is understood to occur in infinite precision and is not an evaluation in the C++ abstract machine. When discussing C++ expressions that are evaluated with C++ semantics, this is specifically noted and the expression is typeset as inline code.

• When an integral scalar object is typeset in mathematical notation, the value corresponds to the numeric value of the object.