Understanding limits to infinity

When x->∞, what is the exact number of x?

We don’t know, x is undefined.

∞ is not a number, is a idea of having a greater number than you give.

When x->∞, 1/x appoachs zero, but is never equal zero!

When n -> ∞, does sin(1/n) / (1/n) have meaning?

I used to thought 1/n = 0 while n->∞, but 0 cannot be divided, So I was confused.