The following cute bit of humor is going about at the moment:
Hahahaha, as my daughters would text. Obviously, a really, really nerdy bit of humor, therefore right up my alley.
But here's the thing, I don't think the top one is fully correct. For example, if I go to Wolfram Alpha and enter lim 1/(x-8) as x->8 it responds with "(two sided limit does not exist)" because you get infinity if you approach it from greater than 8 and decreasing and minus infinity if you approach it from less than 8 and increasing as shown in the following plot.
What do my nerdy readers think? Is it not quite right? Or is it okay? Is the default to always approach the limit from the positive side decreasing? Or from the side that gives you positive infinity? Or what?