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I've been trying to define what a number is and I've come forth with the definition that a number is a mathematical object with certain properties, such as value and that this value is determined by how much greater or less than a number is than 0. I feel like this makes too much sense and it doesn't work though.

David G. Stork
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  • What is your goal here? Are you trying to give an intuitive definition? A philosophical definition? A formal definition? What kinds of things do you want your definition to encompass? (e.g. for you, is a complex number a number?) – Alex Kruckman Apr 04 '20 at 21:23
  • So $i$ is not a number? – Hagen von Eitzen Apr 04 '20 at 21:23
  • I'm looking for an intuitive definition. I'd also add that I am in high school, freshman year –  Apr 04 '20 at 21:26
  • That’s perfectly reasonable, although the value of a number is relative and you can use any reference point other than $0$. – Vishu Apr 04 '20 at 21:33

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This may be valid as the definition of a real number but it won't work for complex numbers. Because complex numbers don't have order, i.e, you can't say one complex number is greater or lesser than another. You'd need to tweak the definition for complex numbers. You may retain the 'mathematical object with certain properties' part though. You can use the complex plane and define the values of numbers using their coordinates in the complex plane.

  • Another question then, are do the numbers have the property of value or are numbers themselves the value? –  Apr 06 '20 at 01:16
  • I think the numbers themselves are the value. But they are still mathematical objects, since they do have properties like--being real or complex, being prime, etc. –  Apr 06 '20 at 11:15