# Can any one example a function that has limit just in one point

1. Dec 7, 2008

can any one example a function that has limit just in one point

2. Dec 7, 2008

### rochfor1

Re: limit

Let f(x)=x if x is rational and f(x)=0 if x is irrational.

3. Dec 7, 2008

Re: limit

can you prove it

4. Dec 7, 2008

### rochfor1

Re: limit

Yup. Pretty easy to see that $$\lim_{ x \to 0 } f( x ) = 0$$, so we just want to show that it doesn't have a limit anywhere else. To show that it doesn't have a limit at $$c\neq0$$, take a two sequences approaching c, one along rational numbers and one along irrational numbers, and use the sequential criterion for limits. If you have trouble with that, post what you've tried and I'll fill in the details.

5. Dec 9, 2008

### snipez90

Re: limit

You could also use epsilon delta. Only numbers for which e > 0 might not be true are irrational x, but then you can just choose d = e.