is an equivalence relation

Note that as defined in the entry Landau notation is an equivalence relationMathworldPlanetmath on the set of all functions from + to +. This set of functions will be denoted in this entry as F.

ReflexiveMathworldPlanetmathPlanetmathPlanetmathPlanetmath ( For any fF, limxf(x)f(x)=1, and ff.

SymmetricPlanetmathPlanetmathPlanetmath: If f,gF with fg, then limxf(x)g(x)=1. Thus:


Therefore, gf.

TransitiveMathworldPlanetmathPlanetmathPlanetmathPlanetmath ( If f,g,hF with fg and gh, then limxf(x)g(x)=1 and limxg(x)h(x)=1. Thus:


Therefore, fh.

Title is an equivalence relation
Canonical name simIsAnEquivalenceRelation
Date of creation 2013-03-22 16:13:16
Last modified on 2013-03-22 16:13:16
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 9
Author Wkbj79 (1863)
Entry type Result
Classification msc 26A12