Where does series collide?

In mathematics a series is what you get by adding the terms of a sequence one after another: the central question is whether the running totals, the partial sums, settle toward a single finite value (the series converges) or instead grow without bound or oscillate (it diverges). Cauchy's 1821 Cours d'analyse de l'École Royale Polytechnique gave the first rigorous treatment, defining the value of an infinite series as the limit of its partial sums and stating the conditions under which that limit exists. The referent here is a single number, the sum distilled from an ordered list, not a run of data spread across time, a loop of wired components, or a set of television episodes.[1]

Unit

One sum, the limit of the partial sums of a sequence

Recovery means

Not applicable

Measured by

Decided by convergence tests (ratio, root, comparison, integral) that check whether the partial sums approach a finite limit

In statistics and forecasting a time series is a set of observations recorded in time order, usually at regular intervals, so that each value is tied to a moment and the ordering itself carries information: analysts look for a trend, for repeating seasonal patterns, and for autocorrelation, the tendency of a value to resemble the ones just before it. Box and Jenkins's 1970 Time series analysis: Forecasting and control set out the ARIMA framework that models such data and projects it forward. The referent is a stretch of time-ordered measurements to be described and forecast, not a single summed number, a wired circuit, or a run of episodes.[2]

Unit

One run of time-stamped observations, indexed by time

Recovery means

Not applicable

Measured by

Characterised by separating trend and seasonality and estimating autocorrelation, then fitted with models such as ARIMA

In electrical engineering a series circuit is one in which the components are joined end to end along a single path, so the identical current flows through every one of them and the voltage divides among them; it is contrasted with a parallel circuit, where the path splits into branches. Kirchhoff's 1847 paper on the distribution of currents in linear networks, in Annalen der Physik, established the circuit laws from which the series rule follows: resistances in series simply add. The referent is a physical wiring layout carrying a current, not a sum of numbers, a table of dated observations, or a broadcast lineup of episodes.[3]

Unit

One conductive path with components in a line, sharing one current

Recovery means

Not applicable

Measured by

Analysed with Kirchhoff's laws and Ohm's law: the series resistance is the sum of the parts, and one current is measured through each