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Is a quantity a number or does it consist of a number and a unit?

To give an example:
Sometimes I read something like „the quantity of good A the consumer consumes is 10“ and sometimes I read something like „the quantity of good A the consumer consumes is 10 units of good A“.

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  • $\begingroup$ You cannot count without units. When you don't have an explicit reference to a unit, then it is there implicitly. "The consumer consumes 10" still means she consumes 10 of something, however it is measured exactly. $\endgroup$
    – BrsG
    Commented Sep 22, 2022 at 16:23
  • $\begingroup$ BrsG You are right if you speak of mathematics applied to something, or of everyday life when you count apples or pears. But the act of counting is also abstract, above all linked to natural numbers, that are the 'abstraction' of counting things. Through them you can count wihout any unit of measure, but only using these 'pure' numbers. $\endgroup$
    – BakerStreet
    Commented Sep 22, 2022 at 17:26
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    $\begingroup$ I’m voting to close this question as off-topic. It might be on-topic at philosophy or math SE. $\endgroup$
    – Giskard
    Commented Sep 22, 2022 at 20:16
  • $\begingroup$ If you are asking specifically about quantities in economics, it would be helpful to edit the question to make that explicit. It's what your example suggests, but your title is so general as to invite answers referring to non-economic contexts. $\endgroup$
    – Adam Bailey
    Commented Oct 22, 2022 at 19:12
  • $\begingroup$ I agree that the question can be referred to a non-economic context, but I think there isn't such a thing as 'quantity in economics' different from quantities in other fields. It is the use of 'quantity' in applications, so an explanation can only point out the difference between applications and pure mathematics. It is difficult to say if the question is on-topic or not, because it is about economics as an application of mathematics, but in that similar to other sciences. But I think that the question can be interesting, $\endgroup$
    – BakerStreet
    Commented Oct 22, 2022 at 23:46

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If a quantity is a pure number or is a number plus a unit of measure depends on the context.

In everyday language, a quantity denotes something that can be measured or counted, and is represented by a number.

In a context of applied mathematics, as economics or physics, as in your example, a quantity is a number together with a unit of measure (the unit of measure can be implicit, as in your example).

In 'pure' mathematics, nowadays, the term 'quantity' is rarely used. It was used in more ancient mathematics. For instance, Cauchy, in the first half of the XIX° century, spoke of 'a quantity that approaches 0' to define an infinitesimal, where 'quantity' stands for what now we call a variable, and represents a real number. But definitions like that were superseded, in favour of more 'rigourous' definitions, that expunged vague and 'ambigous' terms as 'quantity' or 'approaches'.

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