At this time, it cannot be said that f(x) has (exists) limit.
It should be said that f(x) approaches infinity, and some people say that its limit is infinity.
The statement that "infinity is a variable with infinite limit" is obviously wrong.
Infinity is a variable that approaches infinity.
Infinity is an unbounded variable.
It is wrong to say that "unbounded variables are infinite". For example, the sequence 0, 1, 0, 2, 0, 3, 0, 4, …0, n, …
It is wrong to say that "infinite series must be unbounded", for example, (-1) n.