Answer: we don't need the concept of "limit" to shape the question in the first place. This isn't a math language where "perfect continuity" is even defined, let alone necessary. This isn't calculus. So what? Most of math isn't.
So why did you bring in epsilon-delta? That was like mixing apples and furniture.
Why didn't you just say "Can a curve be flat if I define a curve as not being flat?" The answer is clearly, No.