Burning question. Consider the following set: $$A=\left\{\frac{0}{0},\frac{\infty}{\ \infty},\ 0\cdot\infty,\ 1^{\infty},\ \infty-\infty,\ 0^{0},\ \infty^{0}\right\}$$
The A stands for Any Self-Respecting Mathematician's Worst Nightmare. Anyway, if I wanted to know $|A|$, which I sure do, how would I find it? Is $A$ a set of seven indeterminate forms, and therefore $|A|=7$? Or is $A$ equivalent to $\emptyset$ because the quotient of $0$ and $0$ and the product of $0$ and $\infty$ are not things at all? Or, is $|A|=7$ because $A$ is a set containing 7 empty subsets? Send help!
Way overthinking this here. The fact that the elements are not defined numbers is no problem at all, they are still perfectly good as elements. Thus $A$ is a set of indeterminate forms with cardinality $7$.