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I am currently learning more about Maths. However, I am struggling to know the difference of a property and a law.

  • Is a property like an attribute to an operation, such as addition and multiplication, and a law is the rules for it applying?

  • Is it correct terminology in arithmetics?

Thank you.

Steve Woods
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  • It would help your question tremendously if you included some specific examples you've encountered where some things are called properties and other things are called laws, especially any examples where you've wondered if the terminology couldn't be switched. – Barry Cipra Jun 13 '18 at 12:47
  • Well, I've been learning pre-algebra. – Steve Woods Jun 13 '18 at 12:50

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The difference isn't always clear cut, but in general, a property describes the nature of some mathematical object or structure or set... while a law states how these objects do or do not operate.

A property of the even numbers that that when you divide any member by $2$, the remainder is $0$.

The commutative law of addition states that for any real numbers $a$ and $b$, we have $a+b = b+a$, and this law can be applied to other mathematical objects (such as imaginary numbers). One can imagine non-commutative algebras operating on certain mathematical objects...

Think of automobiles. A property of (nearly all) automobiles is that they have four wheels. (There's no law demanding this.) But a traffic law might state that no car can be driven over 70 mph.

David G. Stork
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  • Thank you very much. I still find it hard to understand though. – Steve Woods Jun 13 '18 at 12:54
  • @SteveWoods Honestly I don't see the word "law" used much outside the empirical sciences and tend to associate it with results which either originate from observations in the real world like the law of large numbers or Benford's law. Other than that the distinction between a law and a property seems rather arbitrary to me. – CyclotomicField Jun 13 '18 at 12:58
  • What is your confusion? (Frankly, though, I don't think there's much need to worry about the distinction. I was a professor of math years ago and these kinds of questions never had much import.) – David G. Stork Jun 13 '18 at 12:58
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    we can say that addition has commutative property but when we apply this to two numbers we use commutative law – Vasili Jun 13 '18 at 12:59