Is this limit valid/defined and if so, what is the value of it? I was wondering if the following limit is even defined/valid; if it makes any sense. If so, what is the value of it? If not, why is it not defined/valid?
Define $n$:
$$ab=n$$ for $ a\rightarrow \infty$ and $ b\rightarrow 0$
Sure, this might be a weird question due to its perhaps philosophical nature. Please keep in mind that I am not yet that good at maths, so I would greatly appreciate an "understandable" answer.
Edit: I have read some of your answers. Does the following clarification change anything?
Let $a,b\in$ R
There is no "relation" between the two variables, one cannot be expressed using the other (such as $a=1/b$)
To rephrase the question: If two variables approach infinity and zero respectively, what would their product be (if it can be determined)?

The limit is undefined because it isn't specified at what rate $a$ and $b$ are approaching $\infty$ and $0$ relative to each other.
For example, if you would define $b$ as $1\over a$,then as $a \rightarrow \infty$ and $b \rightarrow 0$, $n \rightarrow 1$
However, if you would define $b$ as $1\over a^2$, then as $a \rightarrow \infty$ and $b \rightarrow 0$, $n \rightarrow 0$
Since the relation between $a$ and $b$ is not given, the limit remains undefined.
If as you mention in the edit there is no relation between $a$ and $b$, then there would be no limit for $n$. If $a$ would grow faster proportionally to $b$ getting smaller, $n$ would get larger, and if $b$ would shrink faster, then $n$ would get smaller. Since $n$ is not closing in on a certain number (or $\pm \infty$), $n$ does not have a limit.
