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You are not logged in. #1 20100128 08:58:33
"Factor Space"I came up with this idea last night while brushing my teeth! A logarithm is just a misspelled algorithm. #2 20100128 09:05:18
Re: "Factor Space"I find this especially cool because it links linear algebra to number theory. Last edited by mikau (20100128 10:39:59) A logarithm is just a misspelled algorithm. #3 20100128 10:40:25
Re: "Factor Space"
I assume you mean prime integers. If that's the case, every integer z is in U. Further, because the exponents can be 1, 1/z is also in U. The result of this is that U = K. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #4 20100128 10:44:50
Re: "Factor Space"this is a hasty response, but doesn't U include sqrt(2) = 2^(1/2), whereas K being rationals does not include sqrt(2)? A logarithm is just a misspelled algorithm. #5 20100128 10:50:05
Re: "Factor Space"no i'm allowing powers to be rational (right?) Last edited by mikau (20100128 13:53:55) A logarithm is just a misspelled algorithm. #6 20100128 15:04:29
Re: "Factor Space"This is correct (why I deleted my last post). You certainly have a subset of algebraic numbers, what I'm now trying to determine is if it's an interesting subset. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #7 20100128 16:12:58
Re: "Factor Space"what exactly are you talking about when you say "invariants". I know the notion of invarients in programming/comp sci but thats about it. A logarithm is just a misspelled algorithm. #8 20100128 16:24:47
Re: "Factor Space"An invariant is anything that is "fact" that holds in the "same" things. In other words, it doesn't change (remains invariant) between two things that are the "same". For example, if two topological spaces are homeomorphic, then their fundamental group is the same. Another rather simple invariant is that if two finite groups are isomorphic, then they have the same size. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #9 20100128 16:37:19
Re: "Factor Space"i unfortunately haven't studied topology or group theory. I take mostly computer science courses these days. *sigh* i miss math! A logarithm is just a misspelled algorithm. #10 20100128 17:04:16
Re: "Factor Space"This is not quite a useful invariant, but it may illustrate the purpose that invariants serve. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #11 20100128 17:52:55
Re: "Factor Space"that makes sense. A logarithm is just a misspelled algorithm. 