## #math - Fri 27 Apr 2007 between 03:27 and 04:06

### NY Lost Funds

 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*xrook2pawn: oops my mistakerook2pawn: i was going group there for a secondrook2pawn: 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 serieser 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 ibouma, 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 irreduciblethis 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 heywhat 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...