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Point Neighborhood Real Function Quantifier Relation Theory Limit Point Null Domain

1	Real Function
1	Point
1	Neighborhood
1	Relation Theory
1	Quantifier
2	Limit Point
2	Null
4	Domain

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Formal Definition Of Landau Notation

Let us consider a domain and an accumulation point $x_0\in \overline D$ . Important examples are $D=\mathbb{R}$ and $x_0\in D$ or $D=\mathbb{N}$ and $x_0=+\infty$ . Let $f\colon D\to \mathbb{R}$ be any function. We are going to define the spaces and which are families of real functions defined on and which depend on the point $x_0\in \overline D$ .

Suppose first that there exists a neighbourhood of such that restricted to $U\cap D$ is always different from zero. We say that $g\in o(f)$ as $x\to x_0$ if