27 Apr '07 11:24>1 edit
Show steps to prove that 1 doesn't = 0. 😉
It can be done, they actually teach you in college, for some.
It can be done, they actually teach you in college, for some.
Originally posted by RamnedIsn't this implied by Peano's axioms for natural numbers?
Show steps to prove that 1 doesn't = 0. 😉
It can be done, they actually teach you in college, for some.
Originally posted by RamnedIt depends on which set of axioms you're starting from.
Show steps to prove that 1 doesn't = 0. 😉
It can be done, they actually teach you in college, for some.
Originally posted by RamnedFor some reason a lot of those who play chess are drawn to the sciences which typically include a heavy load of math in college. I for instance have a major in Computer Science and another major in math (it was only an extra 4 courses).
wow. I bet that I can name 10 - 15 things that you guys just wrote that I do not understand, as a sophomore in H.S.
You guys, if indeed you are correct, must have taken a hardcore college class.
Originally posted by RamnedI too have some math from the university. But I'm more interested in what is calculable and what's not, what is doable with math, the philosophy with the whole thing, the development of math since the days of the old Greeks and beyond, and the great mathematicians of history.
wow. I bet that I can name 10 - 15 things that you guys just wrote that I do not understand, as a sophomore in H.S.
You guys, if indeed you are correct, must have taken a hardcore college class.
Originally posted by CZekeI thought the null set or the empty set are the same thing, a set with no members. How can zero be the empty set?
I'm a math Master's student (one term from getting my M. Math). That's only so relevant here, however -- proving that 0 isn't 1 is really more of a philosophical question. Mathematicians (especially us pure mathematicians) spend a lot of time proving the obvious, but this is a bit much even for us. When we do need a definition for them, it's usually this:
...[text shortened]... early exercise in ring theory to show that 0 isn't 1 unless you're in the zero ring.
Originally posted by CZekeHow you you get from this to addition? As it's not obvious to me that {0, 1} + {0, 1} = {0, 1, 2, 3}, do you just define everything in terms of successors and iterate?
I'm a math Master's student (one term from getting my M. Math). That's only so relevant here, however -- proving that 0 isn't 1 is really more of a philosophical question. Mathematicians (especially us pure mathematicians) spend a lot of time proving the obvious, but this is a bit much even for us. When we do need a definition for them, it's usually this:
...[text shortened]... early exercise in ring theory to show that 0 isn't 1 unless you're in the zero ring.
Originally posted by DeepThoughtI'm a Math student (very nearly graduated even). These things are taught to us in a college "Axiomatic Set Theory". It basically covers the foundations of math starting with the axioms of Zermelo and Frankel.
How you you get from this to addition? As it's not obvious to me that {0, 1} + {0, 1} = {0, 1, 2, 3}, do you just define everything in terms of successors and iterate?