answersLogoWhite

0

The real numbers form a field. This is a set of numbers with two [binary] operations defined on it: addition (usually denoted by +) and multiplication (usually denoted by *) such that:

  • the set is closed under both operations. That is, for any elements x and y in the set, x + y and x * y belongs to the set.
  • the operations are commutative. That is, for all x and y in the set, x + y = y + x, and x * y = y * x.
  • multiplication is distributive over addition. That is, for any three elements x, y and z in the set, x*(y + z) = x*y + x*z
  • the set contains identity elements under both operations. That is, for addition, there is an element, usually denoted by 0, such that x + 0 = x = 0 + x for all x in the set. For multiplication, there is an element, usually denoted by 1, such that y *1 = y = 1 * y for all y in the set.
  • for every x in the set there is an additive inversewhich belongs to the set, and for every non-zero element x there is a multiplicative inverse which belongs to the set. That is for every x, there is an element denoted by (-x) such that x + (-x) = 0, and for every non-zero element y in the set, there is an element y-1 such that y*y-1 = 1.
User Avatar

Wiki User

11y ago

Still curious? Ask our experts.

Chat with our AI personalities

BlakeBlake
As your older brother, I've been where you are—maybe not exactly, but close enough.
Chat with Blake
RossRoss
Every question is just a happy little opportunity.
Chat with Ross
ReneRene
Change my mind. I dare you.
Chat with Rene

Add your answer:

Earn +20 pts
Q: Enumerate the properties of real numbers?
Write your answer...
Submit
Still have questions?
magnify glass
imp