Infinity is a bit like "Ixtlan".

You can keep moving in the general direction without ever really getting "there"

wherever "there" may be. Infinity is more a concept of "ever-increasing", without stop.

Just as, if "something" keeps decreasing, without ever stopping, it never makes it to zero. (You can imagine becoming billions of times smaller than an electron).

If we say

then

and we can compare that to

We cannot define infinity as a value, since whatever value we may consider,

we may consider a larger one. The ratio being set to zero is more a reflection of the "relative ratio" of the "values", one insignificant compared to the other.

Hence, we consider values approaching what we call infinity,

but the calculations of the limits are based on a constant being insignificant

compared to a value that never stops increasing,

that is why constants divided by infinity are allowed to be considered zero,

when deciding on a value for a limit.

What we are really evaluating usually, is a value being "approached", as though we "could" reach it.