Analysis in \(\mathbb{Q}\)
Calculus
Level
3
It is a well-known theorem that if \(f:\mathbb{R}\to\mathbb{R}\) is a differentiable function such that \(f'(t)=0\) for all \(t\in\mathbb{R}\), then \(f\) is constant.
Is it true that if \(f:\mathbb{Q}\to\mathbb{Q}\) is a differentiable function such that \(f'(t)=0\) for all \(t\in\mathbb{Q}\), then \(f\) is constant?
Notations:
- \(\mathbb R \) denotes the set of real numbers.
- \(\mathbb Q \) denotes the set of rational numbers.
by
Victor Moreno Diaz