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- Mon Dec 09, 2013 12:51 pm
- Forum: College / University Level
- Topic: Same functions over the set of rational numbers
- Replies: 6
- Views: 13238
Re: Same functions over the set of rational numbers
On the contrary, assume that the functions $f$ and $g$ are different at some point $\alpha \in \mathbb{R}$. Take $\epsilon = |f(\alpha)-g(\alpha)| >0$. Since $f$ and $g$ are continuous, there exists $\delta > 0$, such that $|f(x)-f(\alpha)|<\frac{\epsilon}{3}$ and $|g(x)-g(\alpha)|< \frac{\epsilon}{...