i don't see what's so bad about them, they're just the limits of the "upper hull" and "lower hull" of your sequence. they're very intuitive ideas, and just have a bit of a strange feeling definition. but as it turns out the definition is basically the same as that for limits, just that it's only bounded by epsilon from above or from below instead of both.
>>11129036liminfs of functions are great. fatou's lemma is a godsend.
