I agree with your last comment. And certainly questions about product metric or product of normed spaces fall under the tag description. Having this tag is probably not ideal, but it is certainly better than having in the same tag, for example, matrix product, categorical product, product of numbers. Whether it would be useful to divide (product-spaces) into smaller tags, I am not entirely sure. BTW if a longer discussion about this is needed, we can
take it to chat. —
Martin Sleziak 1 min ago
Is there a topology induced in $\mathcal P (X)$ for an infinite set $X$?
Intuitively, if $s_1 \supseteq s_2 \supseteq s_3 ...$ and $\bigcap_i s_i = s$ then we could say $s$ is the limit of $\{s_i\}$. But I don't exactly know how to define the open sets to make that formal.
Even better: Is there...
$$\frac{n}{\infty} + \frac{n}{\infty} +\dots = \frac{\infty}{\infty}$$
You can always break up infinity/infinity 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 $0$.
