Revision as of 16:05, 17 July 2008 by JBL (talk | contribs) (This should be merged with continuous)

The notion of Continuity is one of the most important in real analysis, partly because continous functions most closely resemble the behaviour of observables in nature.

Although continuity and continous functions can be defined on more general sets, we will restrict ourselves to $\mathbb{R}$


Let $A\subset\mathbb{R}$

Let $f:A\rightarrow\mathbb{R}$

Let $c\in A$

We say that $f$ is continous at point $c$ iff $\forall\epsilon>0\;\exists\delta>0$ such that $x\in V_{\delta}(c)\implies f(x)\in V_{\epsilon}(f(c))$

If $f$ is continous at $c$ $\forall c\in A$, we say that $f$ is Continous over $A$

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