Re: f is continuous at the point a. Is f defined omkring a?

From: Will Twentyman (wtwentyman_at_read.my.sig)
Date: 06/16/04 

Date: Tue, 15 Jun 2004 21:42:16 -0400

Jesper wrote:

>>>this is the definition of my book for continuity of f at a. Assume
>
> f:A->R
>
>>>where A is an interval.
>>>For all epsilon>0 There is a Delta>0 For all x in A: |x-a|<delta ==>
>>>|f(x)-f(a)|<epsilon
>>>
>>>How can it then be proved that f is defined near a?
>
>
>
>>Your definition only applies to functions which are defined on
>>intervals; intervals contain no isolated points.
>
> how about this piecewise function
> f:[0,10]->R
> f(x)= x^2 for 0<x<1, x^3 for x=5, x^4 for 9<x<10
> then I would say that f is not defined near 5.
> Or is it wrong to write such a function?
>
>

Is that function continuous at 5? Make sure you've satisfied the
conditions of what you are trying to prove. 

-- 
Will Twentyman
email: wtwentyman at copper dot net
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