A limit is a point or level beyond which something does not or may not extend or pass. It is a restriction on the size or amount of something permissible or possible. If a limit does not cross the "invisible line" than it does not exist. If a limit does cross the "invisible line" than it does exist. Taking the limit of a sequence tells us what happens at an infinite point of a sequence; it would be impossible to do it without limits, since we cannot do anything infinite times. Taking the limit of a function at a certain point is also important because it gives us a lot of specific information about the function around the given point. So basically, the limit is very useful, and it is used in almost every branch of math, I think.
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April 2015
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