Ok so in my astronomy lecture today we were told that if we were to observe an object falling onto a black hole, its 'clock' would slow down due to gravitational time dilation - according to the formula

where =the time we would observe on the clock falling in.

=Proper time on the clock

=the schwarzschild radius

r=displacement.

Using this equation, it would seem that at the point the displacement of the object is equal to the schwarzchild radius, we would observe an infinite time. Does this mean we could never see an object truly enter a black hole? Or have I made a stupid mistake?