# Continuity functions (Generalization)

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• Apr 28th 2010, 03:58 PM
rmorin
Continuity functions (Generalization)
A example of function $\displaystyle f:R\to R$ that no satify Lipschitz condition $\displaystyle \lambda$ in all R, but continuous in all R?
• Apr 28th 2010, 04:09 PM
tonio
Quote:

Originally Posted by rmorin
A example of function $\displaystyle f:R\to R$ that no satify Lipschitz condition $\displaystyle \lambda$ in all R, but continuous in all R?

$\displaystyle f(x)=x^2$ ...(Giggle)

Tonio
• Apr 28th 2010, 04:17 PM
Drexel28
Quote:

Originally Posted by rmorin
A example of function $\displaystyle f:R\to R$ that no satify Lipschitz condition $\displaystyle \lambda$ in all R, but continuous in all R?

Quote:

Originally Posted by tonio
$\displaystyle f(x)=x^2$ ...(Giggle)

Tonio

Haha!

I bet he meant uniformly continuous, huh?
• Apr 28th 2010, 04:22 PM
Krizalid
i think it's probably that thing.

but $\displaystyle f(x)=\sqrt x$ on $\displaystyle x\in[0,\infty)$ is a good choice.