Olathe | Try for n = 0..5. n^2 + n = 0 (mod 6) Or with that. |

int-e | yi: it's divisible by some prime that's =2 (mod 3). |

ihope | If you find another... thing with those properties, let me know. |

Olathe | % Table[Mod[n^2 + n, 6], {n, 0, 5}] |

mbot | Olathe: {0, 2, 0, 0, 2, 0} |

ihope | Now, is "isomorphic" the general term for things that are equivalent in some obvious way? |

stork | > 1 + ((3 / 3 ^ 2) * (4-1)) |

mbot | 2.0 |

|Steve| | ihope: A field isomorphism is a ring isomorphism. |

Jan- | I'd say "of the same type", but I'm not going to argue with mathematicians. |

Olathe | So, any time n is 6x + {0, 2, 3, 5} |

stork | yay |

ihope | |Steve|: so no it isn't? |

kilimanjaro | ihope, it doesnt have to be obvious |

stork | i think my infix->postfix translator works :) |

thermoplyae | No, not really |

ihope | Infix? Who uses that junk? :-P |

thermoplyae | Things that are isomorphic are often equivalent in some obvious way, but not the other way around Isomorphisms carry more weight imo |

stork | > 1 + ((3 / 3 ^ 2) * (4-1)) + (1/2) * ((2^4) / 32) |

mbot | 2.25 |

ihope | Saying stuff like "the sum of x and y" rather than "x plus y" means you don't have to say "the quantity" or "parenthesis" all the time. |

|Steve| | ihope: you have to have f(xy) = f(x)f(y) and f(x+y) = f(x) + f(y), f(1) = 1, f(0) = 0, etc, to have a ring homomorphism. To say that two fields are isomorphic means that such an isomorphism exists between them. |

kilimanjaro | Well, whether two objects are isomorphic just depends on what properties you are interested in |

Saizan | stork: do you start with a full-paranthesized expression? |

stork | Saizan, sorry> |

|Steve| | kilimanjaro: He was talking about fields. |

stork | ?* |

mbot | Maybe you meant: . v |

Saizan | stork: translating infix to postfix |

kilimanjaro | |Steve|, right, but you need more than a field isomorphism to talk about the uniqueness of the reals well, maybe |

ihope | Without order, the real numbers are just the rational numbers with lots of extensions. |

|Steve| | stork: You just have to use a stack to build a postfix expression from infix, right? |

ihope | An uncountable number of them, I guess. |

Olathe | Mistake. n^2 + n + 2 = 0 |