Discrete events

Information is often represented as a sequence of symbols. A binary file of length n is a sequence b₁, b₂, …, b_n, where each b_iis a binary symbol, 0 or 1. An English text of length n is a sequence of words w₁, w₂, …, w_n. The file is a function

filename: {1, 2, … , n} ® Bin
The text is a function

text: {1, 2, … , n} ® EnglishWords
A data signal is a sequence

data: {1, 2, … , n} ® SymbolSet
where SymbolSet is an appropriate set of symbols eg. Bin, EnglishWords. Data signals arise in computer storage, computer communication networks.
An event stream or event trace is a record of the significant events that occur in a system of interest. The trace of events in a phone call might be

LiftHandset, HearDialTone, DialDigits, HearTelephoneRing, …
or, if the other phone is busy, the trace might be

LiftHandset, HearDialTone, DialDigits, HearBusyTone, …
An event trace is a sequence

trace: {1, 2, … , n} ® EventSet
The behavior of state machines is described by event traces.