Limit inferior and limit superior are two concepts that help you figure out what happens when a number goes on forever.
Think of them like two people at the end of a line. Limit inferior is the very last person on the line and limit superior is the person standing right in front of them. When you look at an unlimited line of people, you know that there is always one person at the very end (limit inferior) and one person right in front of them (limit superior).
In math terms, the limit inferior is the lowest possible number in a group or sequence of numbers, and the limit superior is the highest possible number. This means if you have a group of numbers that are getting bigger and bigger and don't ever stop, the limit inferior would tell you the smallest number of the group, and the limit superior would tell you the biggest number of the group.