Post by Karl on Aug 4, 2015 18:52:20 GMT
The current text reads:
For each $n \in \mathbb{N}$, let $f_n : \mathbb{N} \to \mathbb{N}$ be defined by $f_n(k) = \frac{n-k}{n+k}$. Is the sequence $(f_n)$ uniformly convergent?
However, I think the quotient $\frac{n-k}{n+k}$ will often not be a natural number. Should the co-domain of $f_n$ be the set of rational numbers?
That is:
For each $n \in \mathbb{N}$, let $f_n : \mathbb{N} \to \mathbb{Q}$ be defined by $f_n(k) = \frac{n-k}{n+k}$. Is the sequence $(f_n)$ uniformly convergent?
Thanks,
Karl
For each $n \in \mathbb{N}$, let $f_n : \mathbb{N} \to \mathbb{N}$ be defined by $f_n(k) = \frac{n-k}{n+k}$. Is the sequence $(f_n)$ uniformly convergent?
However, I think the quotient $\frac{n-k}{n+k}$ will often not be a natural number. Should the co-domain of $f_n$ be the set of rational numbers?
That is:
For each $n \in \mathbb{N}$, let $f_n : \mathbb{N} \to \mathbb{Q}$ be defined by $f_n(k) = \frac{n-k}{n+k}$. Is the sequence $(f_n)$ uniformly convergent?
Thanks,
Karl