But you can divide by arbitrarily small numbers tending down to zero."

Or up to zero, where your result will tend towards minus infinity (meaning it would be infinitely worse than all other Treasure Cards not costing zero). That's the reason you cannot divide by a number tending towards zero without spesifying the direction, and also the reason why dividing by zero would make no sense. Luckily it's prohibited. Remember that the coin cost of Copper is as close to -1 as to 1.

Cards can't cost less than zero, though, so at least in the context of Dominion, 1/0 only gives one answer.

No, it doesn't give an answer, because it's impossible to divide by 0 (and to use your own argument, sort of, we're not having cards with fractions in their cost in Dominion, so the closest we can come is to divide by one, which, of course, doesn't help us immensely).

That being said, an often overlooked fact is that three plays of Copper gives the same net effect as three plays of Silver and three plays of Gold.

Let's say you buy a:

Copper - Cost 0. After one play, you've gained 1 in value. After the second play, you've gained 2, After the third play, you've gained 3.

Silver - Cost 3. After one play, you've lost 1. After the second play, you've gained 1. After the third play, you've gained 3.

Gold - Cost 6. After one play, you've lost 3. After the second play, you haven't lost nor gained anything. After the third play, you've gained 3.

Platinum - Cost 9. After one play, you've lost 4. After the second play, you've gained 1. After the third play, you've gained 6.

In a vacuum, this means that it's not worth it to buy a Silver or a Gold instead of Copper, unless you get to play it at least four times. Platinum is profitable after three Plays, though. With fewer plays, Copper is the best of them. There are always edge-cases, and yes there are a lot of them, especially here. Still, this is something that you should probably know about.