I know that by definition the cartesian product of [a1, b1], [a2,b2], ..., [an. bn] is a rectangle in R^n. Are we "allowed" to call the cartesian product [a1] * [a2, a2] * ... * [an, an] a rectangle in R^n? I know that by definition [a,b] = {x: a <= x <= b}. The set [a1,a1] = {x: a1 <= x <= a1} which is just the singleton set {a1}. Thus the rectangle [a1] * [a2, a2] * ... * [an, an] is just the cartesian product a1*a2*a3*..*an, where each ai is a real number, which hardly looks like a rectangle if we draw it in say, R^2 or R^3.(adsbygoogle = window.adsbygoogle || []).push({});

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Question about rectangles in R^n

Loading...

Similar Threads - Question rectangles | Date |
---|---|

B Secondary Upper and Lower Bound QUESTION | Mar 10, 2018 |

B Find the missing energy value given a set of data (Hypothetical question) | Mar 3, 2018 |

B Simple question about compactness | Feb 22, 2018 |

B Beginner function question | Feb 17, 2018 |

Simple question about rectangles in the plane | Mar 22, 2010 |

**Physics Forums - The Fusion of Science and Community**