It's been a while since I've done serious mathematics so I'm almost certainly wrong about this, but the "logical" definition for a derivative looks incorrect un

It's been a while since I've done serious mathematics so I'm almost certainly wrong about this, but the "logical" definition for a derivative looks incorrect under the section "How do People Understand Mathematics?" (pg 3). Shouldn't the distance between the quotient and d be less than ɛ? http://arxiv.org/pdf/math/9404236v1.pdf http://arxiv.org/pdf/math/9404236v1.pdf