У чым розніца паміж картэжам і паслядоўнасцю ў матэматыцы?


адказ 1:

AsequenceinasetXisafunction[math]NX[/math],where[math]N={1,2,}[/math]isthenaturalnumbers.An[math]n[/math]tupleisafunction[math]{1,,n}X[/math].Usuallythedefinitionofthelatterisnotgivenasafunction,butthetwoconceptionsareequivalent,andIsuspectthepersonaskingthequestionwantedtoknowwhattheconnectionwas;itislength:asequencehas(countably)infinitelength,andatuplehasfinitelength.A sequence in a set X is a function [math] \N \to X [/math], where [math] \N = \{ 1, 2, \ldots \} [/math] is the natural numbers. An [math] n [/math]-tuple is a function [math] \{ 1, \ldots, n \} \to X [/math]. Usually the definition of the latter is not given as a function, but the two conceptions are equivalent, and I suspect the person asking the question wanted to know what the connection was; it is length: a sequence has (countably) infinite length, and a tuple has finite length.