# Continuity definition

1. Feb 16, 2010

### Bleys

I'm just wondering why in the definition of continuity, limit of function, or even just limit of a sequence, the inequality signs are strict? What would happen if you only required that
$$| f(x) - L |\leq \epsilon$$. Or that $$|x-a|\leq \delta$$.

Last edited: Feb 16, 2010
2. Feb 16, 2010

### mathman

Without giving it much thought, I suspect it doesn't matter whether the inequalities are strict or not.

3. Feb 16, 2010

### Bleys

So it was simply decided that the definition had this: it's just convention then? There is no special case that required them to be this way?