A pair is a set of two things of the same type that are used together. What do you call a set of three such things? What about four, five, etc.?
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2I would just use "a set". – user3169 Oct 24 '15 at 4:29
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Related: Collection vs Set – ColleenV parted ways♦ Feb 14 at 15:34
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Three: Triplet, trio, triad, or three-of-a-kind
Four, five, six: Quartet, quintet, sextet. Note that these words are uncommon and sound quirky or formal.
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It's safe to call 'a set of three' or whatever number you want. Why? Because if the context is not clear, it may sound odd.
Here is the list of, for example, set of 'three' in various cases. Note that for each condition, the word is different. While for three kids delivered it's triplet, for a card game, it would be 'trio.' Furthermore, in cricket, it'd be 'hatrick' when three batsmen are out; 'trilogy' for a tri-series movie.
So, again, to be on a safer side, call 'set of ' when the context is not clear. Say, you buy a set of three shelves from some store.
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Threesomes. They say pairings in golf (sometimes twosomes) when there are two in a group. They need to come up with a similar word when there's three. My suggestion is triplings.
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2I would not understand "triplings" to mean three people, but apparently it means "...three babies born from the sperm of one man and one egg donor, but are carried by different surrogates." Source. That's not exactly what the question is asking for. – ColleenV parted ways♦ Jul 19 '17 at 18:14
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Trilogy is what you call a work with a set of three
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I think “trilogy” is too specific as it refers only to to art, usually fiction. – Lucas Nov 24 at 21:00
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Triumvirate: any group or set of three.
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