Limit

Intuition

A limit is a the behaviour of a quantity when a certain parameter moves towards a certain value.
For example, the function $f(x)=\frac{1}{x}$ has a limit $0$ when $x$ goes to infinity : the larger $x$ gets, the smaller $\frac{1}{x}$ becomes. Note that the limit $0$ is never reached in this case.

Specific notions

The term "limit" refers to various notions:

• The limit of a sequence
• The limit of a function
• The limit of a sequence of functions

Unification

All these definitions are particular cases of a general notion of limit, see Limit (topology).