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In a recent discussion, someone told me tuples in the modern meaning (in particular, tuples are heterogeneous: that is, different elements of a tuple can belong to different sets/have different types) first appeared in Codd's tuple calculus. I was surprised it would be so late, but searching Google Books before 1970, I can't see any clearly heterogeneous examples, and quite a few clearly homogeneous ones ("tuple of ones and zeros", "tuple of natural numbers", etc.)

Сan anybody confirm that Codd introduced heterogeneous tuples or point out an earlier appearance?

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    WHat was the "earlier" meaning your title implies?2010-08-25

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Tuples appear in essentially all formal treatments of set theory, and those go back to way before the 70s!

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    And there is a fine example in, e.g., Jacobson's _Lectures in Abstract Algebra_.2010-08-25
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I'm not sure having really understood your question, but it seems to me that mathematicians make no difference between heterogeneous and homogeneous tuples. Consider $\left(5,b,f,8,3\right)$: one can say it is an heterogeneous tuple because the set $\left\{5,b,f,8,3\right\}$ can be partitioned into $\left\{b,f\right\}$ and $\left\{5,8,3\right\}$, letters and digits respectively. But are letters and digits of different type? What do you mean by type? In mathematics, as far as I know, there is only one type: the set type. Everything is a set. In this example letters and digits should be both defined as (particular) sets. So every tuple is homogeneous by default. Also, consider $\left(2,1,9,7\right)$: there are only digits this time, so one can say it is an homogeneous tuple. But what if I split the set of all digits into those less then $5$ (the "low" digit type) and those equal to or greater than $5$ (the "high" digit type)? It becomes heterogeneous. I would say the context is of great importance here.

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    Technically, of course, you are right: everything is$a$set. But I mean things like "consider$a$pair ($n$, a), where $n$ is$a$natural number and a is a letter", or, to use your second example, "where $n$ is a number less than 5 and $a$ is a number equal or greater than 5" would be as good; i.e. where the author explicitly says that different elements should belong to different sets.2010-08-25