Given any set X, a sequence in X is a function f:X from the set of natural numbers to X. Sequences are usually written with subscript notation: x0,x1,x2, instead of f(0),f(1),f(2).

Generalized sequences

One can generalize the above definition to any arbitrary ordinalMathworldPlanetmathPlanetmath. For any set X, a generalized sequence or transfinite sequence in X is a function f:ωX where ω is any ordinal number. If ω is a finite ordinal, then we say the sequence is a finite sequence.

Title sequence
Canonical name Sequence
Date of creation 2013-03-22 11:50:33
Last modified on 2013-03-22 11:50:33
Owner djao (24)
Last modified by djao (24)
Numerical id 11
Author djao (24)
Entry type Definition
Classification msc 03E10
Classification msc 40-00
Related topic ConvergentSequence
Defines generalized sequence
Defines transfinite sequence
Defines finite sequence