Any point in $\mathbb{R}^2$ can be described as the coordinates of the tip of a vector. As any vector can be the hypotenuse of the triangle formed by...
Not quite. Fix $k$. If $n \ge N$ and $x\in \left$, then $\lvert \frac{k}{n} - x\rvert \le \frac{1}{n} \le \frac{1}{N} < \delta$. Thus, for all $n \ge...