#math - Sun 6 May 2007 between 20:26 and 20:32

NY Lost Funds

 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 aroundIsomorphisms 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 realswell, 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