Reversing the Definition of Limit: Does the Error Alter its Meaning?

[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

 

[radou]

Yes, it does. Do you see how?

 

[lith101]

no, please explain

 

[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.