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.
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.