I am taking the limit of a sequence as $n$ approaches $\infty$.
The sequence is a fraction and after taking the limit of both the numerator and the denominator, I get an undefined value over infinity.
The solution to the problem applies the Infinity Property: ${c\over\infty} = 0$
How is it that the Infinity Property can be applied here? Is an undefined number still a constant number?
Not sure exactly what you mean...
I'd to see the sequence you're taking the limit of.
I feel like you're referring to an indeterminate form, L'Hôpital's Rule generally takes care of those.
Infinity is not a number, writing it in such a way in your 'Infinity Property', just doesn't make any sense in context (Purely working within $\Bbb{R}$).
A number can't be undefined, a function at a point can be undefined.
Finally, if you come across an indeterminate form, you must use other methods to take the limit. It's called an indeterminate form because you cannot determine the limit from it.
3 and 4 may seem nit-picky, but definitions in mathematics are important. Especially here, where people will struggle to help you.