What’s five times nothing?

Neither Australia nor New Zealand has a one cent piece, and New Zealand plans to take the 5 cent piece out of circulation as well, leaving 10 cents as the smallest coin. I have often thought that Canada and the US should also withdraw the one cent coin, since such coins only clutter up our change purses and are each worth very little. However, this creates an interesting mathematical dilemma. In the two Antipodean realms there is no such thing as one cent. If so, then the 5 cent coin is worth five times something that does not exist. If 5 x 0 = 0, then are the 5 cent coin and all other sub-dollar coins worthless?