- #1
Yoni V
- 44
- 0
Homework Statement
It is not exactly a homework question, but why does the definition of a limit use strict inequalities as follows:
if 0 < |x - a| < δ, then |f(x) - l| < ε
rather than weak inequalities, for example
if 0 < |x - a| < δ, then |f(x) - l| ≤ ε
Could the addition of the equality option make a difference?
Homework Equations
The Attempt at a Solution
I tried thinking of functions that would yield different limits to the limit produced by the formal definition, but couldn't find any.
I also tried to rule it out somehow with formal deduction, but couldn't.
Any hints or ideas?
Thanks