<P> These notions of a limit attempt to provide a metric space interpretation to limits at infinity . However, note that these notions of a limit are consistent with the topological space definition of limit if </P> <Ul> <Li> a neighborhood of − ∞ is defined to contain an interval (− ∞, c) for some c ∈ R </Li> <Li> a neighborhood of ∞ is defined to contain an interval (c, ∞) where c ∈ R </Li> <Li> a neighborhood of a ∈ R is defined in the normal way metric space R </Li> </Ul> <Li> a neighborhood of − ∞ is defined to contain an interval (− ∞, c) for some c ∈ R </Li> <Li> a neighborhood of ∞ is defined to contain an interval (c, ∞) where c ∈ R </Li>

When does a limit as x approaches a constant fail to exist