Table of Contents - 20.39.7.152. Limits for sequences of extended real numbers
Textbooks generally use a single symbol to denote the limit of a sequence of
real numbers.
But then, three distinct definitions are usually given: one for the case of
convergence to a real number, one for the case of limit to and one
for the case of limit to .
It turns out that these three definitions can be expressed as the limit
w.r.t. to the standard topology on the extended reals.
In this section, a relation is defined that captures all three
definitions (and can be applied to sequences of extended reals, also),
see dfxlim2.