Equation field guide
Subscripts: which member of a family?
A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.
An index is part of the name
x₀ and x₁ are two related quantities, not x multiplied by zero and x multiplied by one. For a sequence, x₀ may be its initial value and x₁ its next value. In a vector, x₁ may instead be the first component. Context decides.
A notation such as C₍pre₎ uses a word-like subscript to distinguish one component of a total C. It should be read as one named quantity.
Bound indices in sums
In Σᵢ aᵢ, the index i tells you which terms to visit. If the bounds are i = 1 through n, add a₁, a₂, and so on through aₙ.
An index inside a sum is a local counting label. It need not have the same meaning as the same letter in a different equation.
Check the range
An index may start at 0 or 1 and may include or exclude an endpoint. Those choices can change a result. Look for the stated range before counting terms or interpreting an average.
When a subscript labels a physical component, check whether it selects a coordinate, a phase, a group, or a measurement condition.