rook2pawn | (because a nonsurjective f, could still have f(1) -> 1) |

TRWBW | rook2pawn: yes, yes, ? |

rook2pawn | and so we could say f(n*1_R) = f(0_R) = 0_S = f(1_R + 1_R + ... + 1_R) = nf(1_R) = n*1_S -> hence characteristic can get preserved between nonsurjective maps |

TRWBW | rook2pawnk: homorphism implies f(0_R)=f(0_S), so if R has characteristic n, then S must have characteristic m|n. for example the homorphism from Z_(ab)->Z_a given by f(x)=b*x rook2pawn: oops my mistake rook2pawn: i was going group there for a second rook2pawn: for example homorphism from Z_(ab)->Z_a given by f(x)=x mod a. rook2pawn: make sense? Z_ab has characteristic ab, Z_a has characteristic a, a|ab |

rook2pawn | Oh okay so it simply happents that n*1_S = 0_S where n is the characteristic from R but n is not necessarily the smallest positive integer that does the job |

TRWBW | rook2pawn: i'm assuming here both rings have units and f(1_R)=1_S and characteristic is the smallest n>0 s.t. n*1=0 |

keoki_zee | quick question to ALL: how does one prove the uniqueness of the multiplicative identity in a ring? |

rook2pawn | let f be the fake identity , 1 the real one. 1 * f = 1, but 1*f = f as well hence f = 1 |

mrgibson | Simple question, I have an apple at a base price of 1$, but for each extra apples I bought the price increase by 10%, If I want for example 20 apples, I can start counting every prices one by one, but I guess a formula can be used ? |

sumpt | mrgibson: if I am not mistaken you can use a geometric series er an arithmetic series |

ddark | what the fuck is the deal with imaginary numbers |

kestas | % Integrate[e^(-1/(x^2+x)),x] |

mbot | kestas: Integrate[e^(-(x + x^2)^(-1)), x] |

bouma | ddark: whats the solution to x^2 +1 =0 |

ddark | i bouma, it is equal to i |

bouma | im just starting to learn about where it comes from more formally in a ring theory subject |

kestas | % Integrate[e^(-(x + x^2)^(-1)), x] |

bouma | interesting stuff |

mbot | kestas: Integrate[e^(-(x + x^2)^(-1)), x] |

kestas | youre not even trying |

ddark | bouma, yeah I'm taking intermidiate algebra right now it sure as hell is more interesting than doing polynomials for an entire semester. |

bouma | basically x^2 +1 , is irreducible, in a similar way to primes being irreducible this leads to alsorts of wonderful things, but its not just pulled from somewhere... although it seems that way until, say, 3rd uni doing pure math.. its a long haul, but if you want to know all the info is avail more readily (books, interweb.. etc) |

mrgibson_ | I just asked a question about apples, someone seen it? |

kestas | % Integrate[(-1)/(x + x^2), x] |

mbot | kestas: -Log[x] + Log[1 + x] |

Ultra5pam | hey what is difference between -1 and -1.0????? |

mrgibson_ | one is unsigned integer and the other is a float? erm signed |

JabberWalkie | Ultra5pam 1-(-1.0)=0 |

Ultra5pam | right. is it 0 or 0.0? |

JabberWalkie | 0....0.0 would be kind of redundant... |