# What’s wrong with this reasoning that ∞∞=0\frac{\infty}{\infty}=0?

You can always break up $\infty/\infty$ into the left hand side, where n is an arbitrary number. However, on the left hand side $\frac{n}{\infty}$ is always equal to $0$. Thus $\frac{\infty}{\infty}$ should always equal $0$.

How do you know $0+0+0+0+...... = 0$? If you think about it $0 + 0 + 0 +..... = 0\times\infty = 0\times 1/0 = 1$. (or any other number). We clearly are dealing with a value on which standard arithmetic doesn’t apply. (Hence “infinity is not a number”.)