# Definition of limit reversed

1. Feb 3, 2010

### lith101

so i have a question. If you reverse the definition of limit, does the error change the meaning?

original: for each epsilon>0, there exists a delta>0, such that if 0<|x-c|<delta, then |f(x)-L|<epsilon.

with an error: for each delta>0, there exists an epsilon>0, such that if 0<|x-c|<delta, then |f(x)-L|<epsilon.

So does this error change the meaning of the definition? thanks

2. Feb 4, 2010

Yes, it does. Do you see how?

3. Feb 4, 2010

4. Feb 4, 2010

### g_edgar

Consider the function f(x) = 1 for all x, c=0, L=2 (and not L=1 as you would expect). Show that this satisfies the new definition, but not the original one.