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Wikipedia defines range of data type:

the set of possible values that that variable can hold.

Suppose we have two data types A and B. Now, with attention to the definition of widening in section 7.4 of Concepts of Programming Languages, we can say:

range of B is larger than A when range of B includes at least approximations of all members of range of A.

But above definition is informal; because "accuracy" of approximation is not determined. For example we can consider 0 as approximate for 0 of int and 1 as approximate for all other members of int. So we give a strange statement:

range of int ≤ range of {0,1}

Although we can add the |A| ≤ |B| as a criteria to avoid some strange statements like above one (|A| means Cardinal number for set A); but the problem of "accuracy" remains again.

Do you know a formal definition for "a data type with larger range"?

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  • $\begingroup$ $1$ being an approximation for all nonzero integers is pretty abusive, though they say that some tribes count with "one, two, many". $\endgroup$
    – user16034
    Commented Sep 9, 2022 at 9:31
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    $\begingroup$ Why do you feel the need for a formal definition ? $\endgroup$
    – user16034
    Commented Sep 9, 2022 at 9:35
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    $\begingroup$ You're placing too much faith in Wikipedia, and in any case you are trying to define formally a phrase that has several possible meanings, of which Wikipedia lists two (range of a numeric type, range of an array). If you seek more formal and more exact understanding, the first step is to not read Wikipedia and open a textbook. We can suggest one if you tell us what you're after in the grander scheme of things. $\endgroup$
    – Andrej Bauer
    Commented Oct 9, 2022 at 10:11

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$$B_{\text{min}}\le A_{\text{min}}\land B_{\text{max}}\ge A_{\text{max}}$$

should do (with the implicit assumption that the types $A$ and $B$ are appropriate to represent numbers).

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  • $\begingroup$ You're assuming that the datatypes in question are linearly ordered and that an inclusion of $A$ into $B$ is understood. $\endgroup$
    – Andrej Bauer
    Commented Oct 9, 2022 at 10:09
  • $\begingroup$ @AndrejBauer: numbers are known to be linearly ordered $\endgroup$
    – user16034
    Commented Oct 10, 2022 at 10:32
  • $\begingroup$ The OP never mentioned numbers (except for cardinal numbers at the end), so at least I never guessed they were discussing numerical datatypes. Also, complex numbers are not linearly ordered, but that's not important. $\endgroup$
    – Andrej Bauer
    Commented Oct 10, 2022 at 12:46
  • $\begingroup$ @AndrejBauer: from the book: "Type conversions are either narrowing or widening. A narrowing conversion converts a value to a type that cannot store even approximations of all of the values of the original type. For example, converting a double to a float in Java is a narrowing conversion, because the range of double is much larger than that of float. A widening conversion converts a value to a type that can include at least approximations of all of the values of the original type." $\endgroup$
    – user16034
    Commented Oct 10, 2022 at 13:12
  • $\begingroup$ I don't think people are required to read books referred to to understand questions. The term datatype is much more general than numeric datatype, and that's how I understood it. In any case – whatever, it's not important, enjoy my upvote. $\endgroup$
    – Andrej Bauer
    Commented Oct 10, 2022 at 15:19

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