Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.

Normal Size Small Size show me how

Normal Size Small Size show me how

# Axioms

### Axioms of addition and multiplication in R. Let a, b, and c denote any real #'s

Term | Definition |
---|---|

Closure Axiom for Addition | a+b is a unique real number |

Associative Axiom for Addition | (a+b)+c=a+(b+c) |

Commutative Axiom for Addition | a+b=b+a |

Identity Axiom for Addition | There exists an element 0∈R such that for each a∈R, 0+a=a and a+0=a |

Axiom of Additive Inverses | There exists an element -a∈R for each a∈R, such that a+(-a)=0 and (-a)+a=0 |

Closure Axiom for Multiplication | ab is a unique real number |

Associative Axiom for Multiplication | (ab)c=a(bc) |

Commutative Axiom for Multiplication | ab=ba |

Identity Axiom for Multipication | There exists an element 1∈R, 1≠0, such that for each a∈R, a·1=a and 1·a=a. |

Axiom of Multiplicative Inverses | There exists an element 1/a∈R for each nonzero a∈R such that 1/a·a=1 and a·1/a=1 |

Distributive Axiom of Multiplication with Respect to Addition | a(b+c)=ab+bc and (b+c)a=ba+ca |

Created by:
100006167281117