This is just not true. The normal limit we have here means a limit would have to exist from both directions and they should be equal. They’re not, so the limit doesn’t exist.
One-sided limits would be denoted by x -> 5– and x -> 5+ or similar.
PS: in complex analysis, there is no distinction between +infty and -infty, so there it would be correct to say the function has limit infty at 5.
You’re right. But in this case, which is the case I was referring to, there is no two sided limit. It is discontinuous. It is in this case which I was referring to. Sorry for not being clear.
In my experience with maths, there’s a whole bunch of different conventions all over the place, so it might’ve genuinely been how they were taught, even if you were taught differently…
This is just not true. The normal limit we have here means a limit would have to exist from both directions and they should be equal. They’re not, so the limit doesn’t exist.
One-sided limits would be denoted by x -> 5– and x -> 5+ or similar.
PS: in complex analysis, there is no distinction between +infty and -infty, so there it would be correct to say the function has limit infty at 5.
You’re right. But in this case, which is the case I was referring to, there is no two sided limit. It is discontinuous. It is in this case which I was referring to. Sorry for not being clear.
In my experience with maths, there’s a whole bunch of different conventions all over the place, so it might’ve genuinely been how they were taught, even if you were taught differently…
Yeah, that’s my experience too. When we did this in school we always defined from which side we were approaching the function.