Razed.

Anyway, Carthage isn't that difficult to learn about. Carthage was settled by Phoenicians, who lived in the general vicinity of modern Lebanon. They had smaller settlements in modern neighboring countries, but they generally lived on the Lebanese coast -- cities like Sidon, Tyre, and Byblos. They are, respectively, the third, sixth, and eighth largest cities of modern Lebanon.

These Phoenicians were traders. They eventually visited a rather large part of the Mediterranean. Basically, if it was a settlement on the Mediterranean coast of Africa, Phoenician traders visited it regularly. Some of these traders stayed to set up permanent missions. Some of these missions evolved into colonies and some of these colonies involved into cities. Carthage (Qart Hadast) was one of these colonial efforts. It wasn't the only such city to evolve on the African coast, but Carthage was the most famous. Eventually, the Phoenician center of power moved to Carthage as Phoenicia itself came under foreign occupation (not terribly unlike how Portugal's power temporarily shifted to Brazil). Carthage then carried on doing much the same as Phoenicia has. And Carthage would go on to found various cities. One such city, founded on the Iberian coastline, was called Qart Hadast. Because of course the Carthaginians decided they needed two cities named Carthage in their empire (and since Qart Hadast just means "New City," the name is especially unhelpful). The Romans would rename this second city Carthago Nova. It, unlike its namesake, would survive Rome's ire. Carthago Nova became Cartagena.

Because the Phoenicians and Carthaginians were so integrated into the Mediterranean trade, and because they settled so many different locations, the razing of Carthage was never going to erase all signs of Carthaginian culture. What this all means is that despite the fact that Rome destroyed the city and then almost immediately built a new city there, there were simply too many traces and records of Phoenician and Carthaginian civilization for the destruction of one city, no matter how grand, to completely erase. Also, Rome's decision to build on top of Carthage's ruins probably did more to erase Carthage's physical legacy than the actual destruction did. Ruins can survive time but they are much less able to survive human construction.

And, of course, the Romans didn't destroy their own records of Carthage. We wouldn't know about their almost pathological obsession with Carthage's destruction if they had. To the Romans, Carthage's conquest and destruction was an abject lesson to the rest of the world -- to erase all evidence of the city's existence and who the Carthaginians were would be to undermine the Roman efforts.

Think of it like this: if you're going to make an example of something or someone, you want people to see what you've done. Otherwise it's not a very good example.