Understanding Infinite Limits: A Formal Definition and Explanation

[tony979]

Homework Statement

Give a definition to explain what it means if the limit of Xn as n->infinity is itself equal to infinity.

Homework Equations

The Attempt at a Solution

It seems the typical use of epsilon to show limits (that we approach arbitrary closeness) doesn't work here, so I had thought I could say it is the opposite of being bounded, but I'm not sure about how to say this more formally...

Thanks for any ideas you may be able to offer

 

[scottie_000]

It seems the typical use of epsilon to show limits (that we approach arbitrary closeness) doesn't work here, so I had thought I could say it is the opposite of being bounded, but I'm not sure about how to say this more formally...

Well you mention the idea of "arbitrary closeness" using the epsilon definition. Why not think about it in terms of the arbitrary "largeness" of xn as n becomes large?
Or try to use epsilon in reverse?

 

[HallsofIvy]

The "the typical use of epsilon to show limits " works fine. It is the "delta" that doesn't work! Saying that a number is "going to infinity" does mean that it is unbounded so instead of "$|x- a|< \delta$" as you would with "limit as x goes to a", how about something like "x> N" for some number N.