Continously differentiable f: R^n --> R^m not 1-1? My course is over with now, but I never could figure out this question. It's pretty much been haunting me ever since, and the internet has not given me a proof that convinces me. My problem is determining why: A continuously differentiable function F: Rn → Rm is not 1-1 when n>m. I can understand why it would be true, I just can't seem to convincingly prove it. Anyone who is familiar with the subject, I would appreciate any feedback.