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

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OlatheTry for n = 0..5.
n^2 + n = 0 (mod 6)
Or with that.
int-eyi: it's divisible by some prime that's =2 (mod 3).
ihopeIf you find another... thing with those properties, let me know.
Olathe% Table[Mod[n^2 + n, 6], {n, 0, 5}]
mbotOlathe: {0, 2, 0, 0, 2, 0}
ihopeNow, is "isomorphic" the general term for things that are equivalent in some obvious way?
stork> 1 + ((3 / 3 ^ 2) * (4-1))
mbot2.0
|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.
OlatheSo, any time n is 6x + {0, 2, 3, 5}
storkyay
ihope|Steve|: so no it isn't?
kilimanjaroihope, it doesnt have to be obvious
storki think my infix->postfix translator works :)
thermoplyaeNo, not really
ihopeInfix? Who uses that junk?
:-P
thermoplyaeThings 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)
mbot2.25
ihopeSaying 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.
kilimanjaroWell, whether two objects are isomorphic just depends on what properties you are interested in
Saizanstork: do you start with a full-paranthesized expression?
storkSaizan, sorry>
|Steve|kilimanjaro: He was talking about fields.
stork?*
mbotMaybe you meant: . v
Saizanstork: 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
ihopeWithout 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?
ihopeAn uncountable number of them, I guess.
OlatheMistake. n^2 + n + 2 = 0

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