A recent answer suggests that some aquarium fish are 'shoal fish' and that there is a minimum number that should be included in a group when adding to your tank.
What are shoal-fish?
If I should not add just one, how many should I add?
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The term 'shoaling' just means that the fish is normally found in very large groups. These species are most comfortable when kept with others of the same kind. Keeping them alone or in very small groups is a source of stress for them, and often causes them to become more aggressive or timid than they normally are.
Some of the most common fish in pet stores are shoaling fish: most tetras, corydoras catfish, danios, mollies, guppies, etc. But bear in mind that many anti-social fish are kept in large numbers in pet store tanks, but should be kept alone or in very small groups at home -- common plecos are an example of that. So "how many should I keep?" is one of the questions you want to have an answer to before you bring a new fish home.
There's no magic minimum number; for some of these species, you'd find thousands in a relatively small area, and you'll never be able to keep that many. Personally, my own preference is to keep at least a half-dozen or so: I feel like this is enough that they'll see lots of others, and any hierarchy that needs to form can be as complicated as it needs to be. More is always better: the social dynamics get more complicated so you see more interesting behavior, and it's really neat to watch a tight shoal dart from one side of the tank to another.
My bare minimum is three, since I figure each fish can see "that guy" and "that other guy". I wouldn't be comfortable keeping this few long-term, but it's what I'd encourage someone to consider if they already have one shoaling fish but not much tank space.
Technically speaking, a shoal is a large social group of fish, though not quite what we'd call a school. The difference is that a school of fish acts more or less in unison, while a shoal is not quite so organized. In the aquarium hobby, you'll often hear the two terms used interchangeably despite the distinction; offhand I'd say most freshwater species in the trade tend to shoal rather than school.
Not all social fish are shoaling fish, and in these cases more is not always better. Some species do best in mated pairs or harems (one male, several females), and any others that stray into their territory are not tolerated. Many dwarf cichlids are a good example of this. Other aquarists will often have rules of thumb that guide the exact numbers you should keep together, like "each group should be 2-3 females per male, with a territory about a foot in radius".
Also, some species will form large aggregations, groups that don't really have much social interaction going on. The distinction here is sort of like going to the mall: you're surrounded by a thousand people, but you don't actually know any of them; you're just all there for the same reason. I'd still try to keep a group of these if you come across any, but it's probably not as necessary.