Mathematics Weblog

Zero

Sunday 29 February 2004 at 12:48 pm | In Articles | Post Comment

Why is ?
By looking at $\displaystyle\lim_{x\to 0}0^x$ and at $\displaystyle\lim_{x\to 0}x^0$ what can you say about ?
Can $\sqrt[0]{x}$ (the zero^th root of x) be defined? If so, how; if not, why?
Criticise the following ‘proof’: If $n\in\mathbb{Z}$ then $\displaystyle\lim_{n\to 0}\frac{n}{n}=\frac{\displaystyle\lim_{n\to 0}n}{\displaystyle\lim_{n\to 0}n}=\frac{0}{0}=1$