Does a "limit" of "infinity" mean "no limit", or just no "convergent" limit

Question

Another user brought this to my attention.

Dang it, forgot the "?" mark.

Answer 1

Technically when a sequence or function or whatever your limit is increases without bounds there is no limit. You can also say it does not converge to a particular value. Very technically speaking a limit cannot be infinity, but this is often used as shorthand for saying 'increases without bound.'

Be careful though, as not converging may correspond to an oscillation, such as the sine function. It doesn't increase without bound, but it doesn't converge either.

Also, you can think of a function going to infinity as having "no limit." The sky is the limit!

Answer 2

Calculus:

Infinity is not a limit, it would be unbounded. In order to have a limit it must meet certain criteria otherwise the limit fails to exist: 1) from the left and the right their is only one limit 2) It can not be oscillating 3) It must be unbound.

Now if your are asking about a limit of a function that question would have a different answer. So... if you could be more specific... that would make things a little eassier.


Cheers,
Alk

Answer 3

Infinity has no value; it means "larger without limit". There is really no concrete distinction between having no limit and having no convergent limit; those are synonyms.