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I surrounded Belgrade with crossbowman and unleashed fire every turn. Its health was near nothing, but my attempts to damage the city's defenses froze or something. When it says '-1' or '-3' usually, it now says nothing, yet I still fire (the whole fire-bolt animation).
I am fairly new at any Civ game, I bought it yesterday. Am I missing something? Why can't I capture the city?
In Civilization V, only melee units can take over a city. Ranged units are important in allowing you to reduce the city health without taking damage in return, but the final attack must be made by a melee unit. (Regarding the missing damage indicator, once a city is down to minimum health, further ranged attacks do not do any damage.)
So, send in a Warrior / Horseman, or whatever you have at the technology level you are at.
Reducing a city below 0 health with ranged attacks doesn't destroy it. Assuming you want to take over the city, reduce it to 0 with melee units and you will take control of it.
If you really don't want a city, there are two ways to destroy cities (but neither will work here- see below):
The first is to capture the city and choose to raze it. This will reduce its population by 1 per turn until it reaches 0 and is destroyed.
The second is to drop a nuclear missile (not a bomb) on a small enough city (4 pop or less). This will completely destroy it. Using multiple nuclear missiles will reduce the population each time if you hate a city that much.
Note that neither of these will work on City States as they are unrazeable. It is impossible to destroy City States, original capitals, holy cities, or Indonesian spice cities.
