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 (expounded)

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

Closure prop. of Addition | For any a and b in R, the sum a+b is in R. |

Closure prop. of Multiplication | For any a and b in R, the product a・b is in R. |

Associative prop. of Addition | For any a, b, and c in R, (a + b) + c = a + (b + c). |

Associative prop. Multiplication | For any a, b, and c in R, (a ・ b) ・ c = a ・ (b ・ c). |

Commutative prop. of Addition | For any a and b in R, a + b = b + a. |

Commutative prop. of Multiplication | For any a and b in R, a ・ b = b ・ a. |

Distributive prop. of Multiplication over Addition | For any a, b, and c in R, (a + b) ・ c = (a ・ c) + (b ・ c). |

Multiplicative Identity | There is a unique number 1 in R such that for any a in R, a ・ 1 = a. |

Reflexive prop. of Equality | For any a in R, a = a. |

Symmetric prop. of Equality | For any a and b in R, if a = b, then b = a. |

Transitive prop. of Equality | For any a, b, and c in R, if a = b and b = c, then a = c. |

Addition prop. of Equality | For any a, b, and c in R. if a = b, then a + c = b + c. |

Multiplication prop. of Equality | For any a, b, and c in R. if a = b, then a ・ c = b ・ c. |

Created by:
natureworld