What are the 6 properties of a real number?

Answer 1

The set of Real numbers is a group with the operation addition. This implies the following properties for all x, y and z that are real:

• Closure: x + y is real.
• Associativity: (x + y) + z = x + (y + z).
• Identity: There exists a Real number, called the additive identity and represented by 0, such that 0 + x = x = x + 0.
• Invertibility: There exists a Real number, denoted by "-x", such that x + (-x) = 0 = (-x) + x.

In addition, the set of Real numbers is a ring and this means that the set is:

• Commutative: x + y = y + x

There is a second operation defined on the set, multiplication, such that multiplication is distributive over addition.

• Distributivity: x*(y + z) = x*y + x*z.

Finally, the set of Reals is a field so that division by non-zero elements is also defined along with the properties of multiplicative identity and inverses.