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We usually say (3,4,5) , (5,12,13) as Pythagorean triples. What is much better way to refer those sets of numbers, Pythagorean triples or Pythagorean triplets?
According to the normal usage we say triple beds, triple rooms, triple jump when we want to give the meaning of three times of a unit. But in the case of Pythagoras theorem we have sets of three integers. Is it not much appropriate way to say Pythagorean triplets for those sets of numbers as in the case of using triplets when you refer three babies. I think in the case of babies we consider a set of three babies and not three times of one baby. What you have to say just to ignore the difference of the two terms or use it much meaningfully. I'm raising this issue here because I have seen the wording Pythagorean triples frequently in many articles.

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  • $\begingroup$ One can say those are synonymous and you can use them whatever way you like but synonymous also can have slightly different meanings which limits their usage. When considering the triplet of synonymous ( hard, tough, difficult) you can say a hard question or tough question or difficult question but can you say difficult surface instead of hard surface ? When you say triplets of babies it gives idea of set of 3 babies born together and when you come to ( 3,4,5) can't you say it's a set of 3 numbers born together satisfying the Pythagoras theorem.. $\endgroup$ Apr 20, 2023 at 3:13

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The word “triple” is appropriate here because $(3,4,5)$ is a tuple consisting of three elements.

In mathematics, a tuple is a finite ordered list (sequence) of elements... Mathematicians usually write tuples by listing the elements within parentheses "( )" and separated by a comma and a space; for example, (2, 7, 4, 1, 7) denotes a 5-tuple.

The term originated as an abstraction of the sequence: single, couple/double, triple, quadruple, quintuple, sextuple, septuple, octuple, ..., $n$‑tuple, ..., where the prefixes are taken from the Latin names of the numerals. The unique 0-tuple is called the null tuple or empty tuple. A 1‑tuple is called a single (or singleton), a 2‑tuple is called an ordered pair or couple, and a 3‑tuple is called a triple (or triplet).

The word “triple” in “Pythagorean triple” is a noun synonymous with 3-tuple, not an adjective. The word “triplet” can also be used in this sense.

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  • $\begingroup$ You are suggesting both give the same meaning, but as I mentioned we don't say triple babies or triplets of beds. There should be different in meanings or convention. $\endgroup$ Apr 12, 2023 at 12:34
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    $\begingroup$ @JanakaRodrigo Words in mathematics often have specific meanings that differ from their colloquial meanings. Also, in colloquial English, “triplet” can mean “one of three,” e.g. “he’s a triplet, he has two siblings that were born at the same time as him.” The established usage in mathematics is that the noun “triple” refers to an ordered list of three elements. $\endgroup$ Apr 12, 2023 at 12:39
  • $\begingroup$ Does triplet mean one element of a set of three elements or one set of three elements in mathematics . $\endgroup$ Apr 12, 2023 at 12:50
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    $\begingroup$ To add: several online dictionaries indicate that 'triple' is in some British and American usages a genuine noun (as opposed to the above more idiomatic meaning as "one of three") synonymous to 'trio' and 'triad'. $\quad$ (Of course, 'triple' is also a verb, as in to triple a bet.) $\endgroup$
    – ryang
    Apr 12, 2023 at 15:47
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    $\begingroup$ Yes, you can argue that. If you tried to argue it was the only correct meaning, though, you'd be wrong, as others have explained in several ways. $\endgroup$
    – Nij
    Apr 13, 2023 at 0:24

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