fish numbers is normally divided into 4 groups..... you either keep a single specimin, a trio (1m x 2f), a pair (1m x 1f) or a group of 6+.
Neatly put, I never thought about it that way. Just to add to that:
the reason for assigning different species to different size groups is their natural behaviour.
Some fish are schooling fish, which need to be kept in groups to feel safe. This includes tetras, danios, rasboras and many barbs. These get a feeling of safety by looking round and seeing others like them; if they can't, they will get stressed. Additionally, group-living fish often develop a very strict hierarchy within the group. This is another strong reason for not keeping the group too small as it means that the top dog will constantly be chasing weaker members to keep his (or her) position. If the group is large enough his aggression will be spread out, but if there are only one or two other group members they may succumb to the stress of getting it in the neck all the time. There are some fish - such as corys- which school for reasons of protection and sociability (if this is not too anthropomorhic a term), but which do not keep to a group hierarchy- these can be kept in groups of 3+, though the more the merrier.
When fish recommended for keeping in a trio, what is usually meant is 1 male and 2 females. These are fish where the male is very territorial and will not tolerate other males, but is quite happy with a little harem. Common fish include gouramis. The reason a trio is recommended and not a pair is that the males of such species may drive their females rather hard, so it is a good idea to keep more than one female to take the pressure off. The number three is not set in stone- 1 male and 3 or more females will do just as well. Livebearers such as guppies, platies, swordtails are also good harem fish, though with most of these you can keep more than one male as long as they are outnumbered by the females. Swordtails are easiest to keep with only one male and a harem of females. It should be added that all these trio fish can be kept as a group of females only- the only reason this is seldom recommended is that the females tend to be less colourful.
Then there are fish that form mated male-female pairs- this includes many cichlids, such as angels and kribs. Here an extra female can actually cause problems as the pair try to drive her out of their territory. The usual method is to start off with a group of mixed-sex juveniles, then as they mature and two form a pair to rehome the rest.
And finally there are fish that are so territorial that you can really only keep one specimen (unless you have a very large tank). These are fish that in the wild would only come together for mating, then drive each other off afterwards- not a viable situation in a fishtank where there is nowhere for the weaker fish to go. This group includes red-tail black sharks of both sexes and male bettas (female bettas can be kept together in a sorority group).