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*was*the value.

This is a point of confusion for me and I cannot marry this up with definitions of the term 'number' that I can find in learned texts.

Is the term itself just abit vague anyway, and can be used willy-nilly, or is there a concise, comprehensive and exclusive definition of the term?

My copy of Chambers Dictionary of Science and Technology says;

Number (Maths.). An attribute of objects or labels obtained according to a law or rule of counting.

which has been regarded here on Physics Forums as

*very imprecise*.

McGraw-Hill says;

number [mathematics] Any real or complex number.

which is amusingly circular, but rather useless in this context.

General dictionaries often refer to 'number' as integer values only too, which is consistent with the term 'number theory' (

*"The study of integers and relations between them"*).

Here is a typical dictionary entry, though this one also extends the definition to other 'mathematical objects';

num·ber (nmbr)

n.

1. Mathematics

a. A member of the set of positive integers; one of a series of symbols of unique meaning in a fixed order that can be derived by counting.

b. A member of any of the further sets of mathematical objects, such as negative integers and real numbers.

2. numbers Arithmetic.

3.

a. A symbol or word used to represent a number.

b. A numeral or a series of numerals used for reference or identification: his telephone number; the apartment number.

Wikipedia possibly muddies the waters further with;

A number is a mathematical object used to count and measure. A notational symbol that represents a number is called a numeral but in common use, the word number can mean the abstract object, the symbol, or the word for the number.

which sounds to me like a number is neither the measure nor the representation but is some notional connection between the two.

Can we arrive at a 'Physics Forum' definition of 'number' that is a concise, comprehensive and exclusive definition of the term (whether or not it actually agrees with external reference texts) or is it just a bit nebulous and cannot be defined, which would be odd for the single most important concept in a subject as precise as mathematics!?