Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20080602 06:25:44
Irrational number with predictable patternI've been thinking about irrational numbers recently (my job doesn't require much brain power) and it occurred to me that there can be rational numbers with predictable patterns. Any number with repeating decimals can be written as a fraction: There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction. #2 20080602 06:34:13
Re: Irrational number with predictable pattern
I don't know about any official name, but I call it the "number of everything". Translating it into binary and then ascii, every single play that Shakespeare wrote is in that number. Every single mathematical proof/definition/axiom is also in that number. "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..." #3 20080602 10:32:04
Re: Irrational number with predictable patternI guess that makes sense, because all of the possible strings appear in there. That's really cool, I didn't think of it that way. Does that mean that both pi and e appear in there completely (I'm not just talking 3.14159265358979, I'm talking the whole thing) or does that only include finite works (like Shakespeare)? There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction. #4 20080602 11:59:44
Re: Irrational number with predictable pattern
What would happen if pi did appear in there completely?
What's your definition of useful? No matter what it is, as far as I know, no. But that's only as far as I know. "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..." #5 20080602 12:41:13
Re: Irrational number with predictable pattern
Well my next point would be that if both pi and e were contained in that number entirely, then that means one of them has to contain the other, and that logic could be expanded to contain all irrational numbers... That just seems wrong. There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction. #6 20080614 10:01:54
Re: Irrational number with predictable patternIt doesn't cover everything but many such examples are covered by Liouville numbers, all of which are transcendental. 