In another thread, I was shot down for saying that a number was a representation of a value. I was told that the number 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; which has been regarded here on Physics Forums as very imprecise. McGraw-Hill says; 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'; Wikipedia possibly muddies the waters further with; 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!?