In case it wasn’t clear from musings on series, these posts are collections of themed material that individually don’t make full posts.

1. There are many ways for a limit to fail to exist. It could be infinite, oscillate within a finite interval, completely devolve into radio static, or simply give you different values when you approach from the right or the left.

2. It is worth restating that a limit of infinity is just shorthand for “the limit is undefined, but in a special way.”

3. Proving the existence of a limit using the delta-epsilon definition involves working backwards. In the actual proof, you say “given epsilon, take delta < [function of epsilon]" and then show that value of delta works. Behind the scenes, though, you have to determine the appropriate function of epsilon by reverse-engineering it from the desired inequality on the function.