- #1
breez
- 65
- 0
Why are limits of functions not defined at non-accumulation points?
For example, take the function f(x) = k, for x in Z
Then based on the epsilon delta definition of a limit, for any epsilon > 0, we can always find a delta, for which 0 < |x-x_0| < delta implies |f(x)-k| = 0 < epsilon. Thus, the limit of every non-accumulation point of f(x) has limit = k.
This example seems to contradict the fact that limits are undefined at non-accumulation points.
For example, take the function f(x) = k, for x in Z
Then based on the epsilon delta definition of a limit, for any epsilon > 0, we can always find a delta, for which 0 < |x-x_0| < delta implies |f(x)-k| = 0 < epsilon. Thus, the limit of every non-accumulation point of f(x) has limit = k.
This example seems to contradict the fact that limits are undefined at non-accumulation points.