In everyday language, the word "limit" is used to describe the boundaries beyond which some quantity or some idea or some thing can't exceed. For example, the speed limit tells you the maximum rate you're legally allowed to drive. And your credit card limit tells you the maximum balance you can carry. Both of these quantities represent upper boundaries. Of course, limits can also apply to lower boundaries. For example, the GPA cutoff put in place by a college's admissions committee or the minimum credit score required for a loan.
In math, the idea of a limit is kind of the same … but it's also kind of different. It's the same in that a limit is used to talk about what happens as you get closer and closer to some condition or boundary. But it's different in that it isn’t necessarily about the minimum or maximum values associated with these things. Instead, in math, the idea of a limit and the type of boundaries it deals with can be much more abstract.
So, how do limits in math work? And why do they matter? We're about to find out.