Ivan Shishkin, Birch Grove

Limit

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8/7/2026, 8:35:49 PM · Ancient Tree

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##### 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|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)|Limit (topology)]].