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People sometimes make a distinction between continuous mathematics and discrete mathematics.

  • Continuous mathematics study objects that abstract the notion of a continuum and typical examples are the set of real numbers $\mathbb{R}$, the complex numbers, and the objects they are used to describe (e.g. manifolds).
  • Discrete mathematics study objects that can be labelled by integers and typical examples are the set of integers, the finite sets or basically everything studied in theoretical computer science (the possible states of a Turing Machine are countable).

My question is about the word discrete: where does it come from? why is it used to describe such a property?

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    $\begingroup$ See discret: "From Old French discret, from Latin discrētus, past participle of discernō (“divide”), from dis- + cernō (“sift”)." And in turn Latin verb discernō is I separate, set apart, divide, part. $\endgroup$ Oct 6, 2023 at 13:09
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    $\begingroup$ Etymology and "people making distinctions" are two different things. People make the distinction largely because of modern curriculum labeling:"In university curricula, discrete mathematics appeared in the 1980s, initially as a computer science support course; its contents were somewhat haphazard at the time." They needed a label to mark a new fashionable area, then some philosophizing was attached to make it more presentable and "continuous" was used for contrast. $\endgroup$
    – Conifold
    Oct 6, 2023 at 23:17

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From the unabridged Oxford dictionary, the usage in English dates back to 1600s.

< classical Latin discrētus separate, distinct, in post-classical Latin also specifically in music (1630 in the passage translated in quot. 1664 at sense A.1b), use as adjective of past participle of discernere discern v. Compare Middle French, French discret (feminine discrète, †discrete) different, distinct (early 14th cent.), (in mathematics) discontinuous, composed of distinct units (2nd half of the 14th cent. in quantité discrete). Compare discretion n. III Compare also earlier discreet adj. and see discussion at that entry.

1660– Belonging to, relating to, or dealing with distinct or disconnected parts; (Mathematics, of proportion) = discontinual adj. 2.

Quote: All Geometrical proportion is either discrete, or continued. Discrete is, when the similitudo rationum is only between the 1. and the 2. and the 3. and 4. term.

Reference: Roger Coke • Justice vindicated from the false fucus put upon it, by Thomas White gent. Mr. Thomas Hobbs, and Hugo Grotius: As also elements of power & subjection; wherein is demonstrated the cause of all humane… • 1660. London, Printed by Tho. Newcomb for G. Bedell and T. Collins, at the Middle-Temple-Gate, Fleetstreet Roger Coke (c1628–?1707)

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It is just the usual English sense of the word discrete. See the Wiktionary definition

Separate; distinct; individual; non-continuous.
a government with three discrete divisions

That can be perceived individually, not as connected to, or part of, something else.

The entry then goes on to give a number of technical definitions including one similar to the one you are interested in. Note that there is also a word discreet which is completely different.

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