My understanding of the user-documentation is that infinity is not allowed as a limit point. But this error message implies that a limit point can be infinity:
limit(x,x,[2,inf]);
limit: third argument must be a finite value or one of: inf, minf, infinity; found: [2,inf]
-- an error. To debug this try: debugmode(true);
But look at
(%i16) limit(cos(x),x, infinity);
gruntz: direction must be 'plus' or 'minus'; found: false
Here the error message is surprising.
(Yes, of course: My use of limit point is distinct from its topological meaning--by 'limit point', I only mean the third argument to 'limit'.)