# Help with limit expression

1. Nov 1, 2005

### daniel_i_l

Is it correct to think about the expresion:
"the limit of f(x) is b when x->a" as saying that for every x thats very close to a but not a (in the deleted neighborhood of a) there is a f(x) thats very close to b (in the neibourhood of b) - or is that not precise enough?

2. Nov 1, 2005

### Galileo

It's definately not precise enough for a mathematical definition. What do you mean by 'very close to a'. What is 'very close'?
The idea of $\lim_{x\to a}f(x)=b$ is that you can make f(x) as close as you want to b by choosing x close enough (but not equal to) a. By close I mean that the distance |f(x)-b| can be made as small as we want. How small? Smaller than any given positive number.

http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/preciselimdirectory/PreciseLimit.html

3. Nov 1, 2005

### whozum

Might want to use 'gets closer' instead of 'is close to'

Thats pretty much the epsilon delta method.

4. Nov 1, 2005

### daniel_i_l

Thanks guys for making that clear.