Infinity in engineering is an immensely productive way of analyzing problems by recognizing infinity.
Entropy is always increasing in the universe, which presents the paradox of decreasing entropy as one goes backwards in time. At the Big Bang, entropy would have impossibly been the lowest of all.
This dilemma is solved if there is infinite entropy in the universe, now and at the beginning.[1]
An open circuit is best defined as "infinite resistance."
The Earth has infinite capacitance.
Also, when there is infinite capacitance in an electric circuit then "all frequencies > 0 Hz will be passed equally, which means that your input AC signal will not be distorted."[2]