What are poles and zeroes (with respect to the inputs and outputs of a system)? I get it, about poles and zeroes, when we talk in terms of the transfer function.

But, if the transfer function is the ratio of the output to the input, then if the input signal is zero, then the gain should go to infinity, right?

Am I missing something?
A transfer function is defined as the ratio of the transform of output to the transform of input where all initial conditions are zero.