PokerPacker Posted April 4, 2009 Share Posted April 4, 2009 Dude, it's infinity. :whoknows: you ever take discrete math analysis or anything like that? infinity isn't just infinity. for example: infinity __ \ /__k =a k=1 infinity __ \ /__k =b k=2 a= 1+2+3+4 + ... + infinity b= 2+3+4+5 + ... + infinity a-b = 1 waah? but a = infinity and b= infinity! Link to comment Share on other sites More sharing options...
Spec138 Posted April 4, 2009 Share Posted April 4, 2009 Lets say we have a set of numbers {1, 2, 3}. The power set of that set is the set of all subsets of that set. So the power set of {1, 2, 3} consists of the elements: {}, {1}, {2}, {3}, {1, 2}, {1,3}, {2, 3}. {1, 2, 3}. Notice that the original set had 3 elements and the power set has 8 elements. This is not just by accident, but for any set of size n, its power set will be of size 2^n. And whats more is that for any n, we know that the size of the power set of that set is strictly bigger than the size of that set. So suppose we had an infinite set, say the set of all positive numbers. How big would the power set of that be? Well from what I just said, its gonna be bigger than the size of the original set. So its gonna be bigger than infinity. So there's a 'bigger' infinity than infinity. And there's an even bigger infinity than this bigger infinity, and an even bigger one and so on and so forth. Once again, you can't quantitate infinity, which is what you're doing here. It's not a normal number. All the values between .000001 and .00001 is equal to the amount of values between -infinity and infinty, infinity. Link to comment Share on other sites More sharing options...
Thinking Skins Posted April 4, 2009 Share Posted April 4, 2009 An infinite amount of anything can't have anything "on the end". It doesn't end. Sure it can. There is an infinite amount of time in between any two seconds (cause we can represent time on the real line and there are infinitely many numbers between any two numbers), but we know that at the end of that last second, there will be another second (just like there is an infinite list of numbers between 0 and 1, but at the end of that list is 1). Link to comment Share on other sites More sharing options...
PokerPacker Posted April 4, 2009 Share Posted April 4, 2009 Sure it can. There is an infinite amount of time in between any two seconds (cause we can represent time on the real line and there are infinitely many numbers between any two numbers), but we know that at the end of that last second, there will be another second (just like there is an infinite list of numbers between 0 and 1, but at the end of that list is 1). there's not an infinite amount of time between any two seconds. that is capped by those two seconds. There are, however, an infinite number of moments between any two seconds. Link to comment Share on other sites More sharing options...
Spec138 Posted April 4, 2009 Share Posted April 4, 2009 Sure it can. There is an infinite amount of time in between any two seconds (cause we can represent time on the real line and there are infinitely many numbers between any two numbers), but we know that at the end of that last second, there will be another second (just like there is an infinite list of numbers between 0 and 1, but at the end of that list is 1). There is only 1 second between two seconds. There's an infinite number of points in a time line between the two though. That still doesn't quantitate infinity though. Link to comment Share on other sites More sharing options...
Thinking Skins Posted April 4, 2009 Share Posted April 4, 2009 Once again, you can't quantitate infinity, which is what you're doing here. It's not a normal number. I'm not quantiting infinity. I'm looking at the power set of a set. And what I'm saying is that there are always more subsets of a set than there are members of the original set. All the values between .000001 and .00001 is equal to the amount of values between -infinity and infinty, infinity. True, but the number of numbers betwen .000001 and .00001 is bigger than the entire set of integers numbers. There is an ordering on infinities, and the smallest infinity is countably infinite (which is the size of the integers). Its a question as to what the 'next biggest' infinity is, but we know that the size of the real numbers is strictly bigger than the size of the integers. Link to comment Share on other sites More sharing options...
PeterMP Posted April 4, 2009 Share Posted April 4, 2009 Once again, you can't quantitate infinity, which is what you're doing here. It's not a normal number.All the values between .000001 and .00001 is equal to the amount of values between -infinity and infinty, infinity. Take the infinite set of numbers. I'm going to break them into two groups. The first group contains one thing (1). The second group contains all other numbers. It must contain an infinite set of numbers, but: (all infinite numbers) > (all infinite numbers except 1) Link to comment Share on other sites More sharing options...
Thinking Skins Posted April 4, 2009 Share Posted April 4, 2009 there's not an infinite amount of time between any two seconds. that is capped by those two seconds. There are, however, an infinite number of moments between any two seconds. whatever you want to call them, there are infinite number of somethings between two seconds. there are 10 deciseconds, and 100 centiseconds, and 1000 milliseconds, and you can keep getting smaller and smaller. If we represent time on a real line, then just like there are an infinite number of numbers between any two numbers there are an infinite number of time units between any two seconds. Link to comment Share on other sites More sharing options...
PokerPacker Posted April 4, 2009 Share Posted April 4, 2009 Take the infinite set of numbers. I'm going to break them into two groups. The first group contains one thing (1). The second group contains all other numbers. It must contain an infinite set of numbers, but:(all infinite numbers) > (all infinite numbers except 1) see my post with the Riemann sums Link to comment Share on other sites More sharing options...
Thinking Skins Posted April 4, 2009 Share Posted April 4, 2009 more math less politics!!!! I so agree. I feel like I'm teaching smart kids like me back when I was in school. Link to comment Share on other sites More sharing options...
velocet Posted April 4, 2009 Share Posted April 4, 2009 Hey Velocet did you get your package? No, I have to wait for the owner of that p.o. box to retrieve it for me. I'll let you know, thanks again. Funny you caught me reading this thread. It's actually relevant to a new book I just got, Naming Infinity by Loren Graham and Jean-Michel Kantor. velocet Link to comment Share on other sites More sharing options...
Thinking Skins Posted April 4, 2009 Share Posted April 4, 2009 the difference between y<1 and y <=1 is the same as the difference between .99999 repeating. The difference is infintessimally small and cannot be recorded in a discreet manner, but it the distinction does exist..9999999 repeating to infinity is a solution for the inequality y<1. 1, however is not a solution for such inequality, it is a solution for the inequality of y<=1. Since they cannot be used interchangeably, they are not the same number. But we have the additive inverse property of the real numbers. This says taht for all real numbers x, there exists a real number y such that x + y = 0. So lets go by your assumption. You claim that .9999999 (repeating) satisfies the inequality x < 1. Then x - 1 < 0. Then by the additive inverse of real numbers (since .99999999 (repeating) is a real number and real numbers are closed under subtraction (implying that x - 1 is a real number)), there exists a y such that x - 1 + y = 0, which implies that x + y = 1. Then you can refer to my post above to see why this leads to a contradiction. Link to comment Share on other sites More sharing options...
Larry Posted April 4, 2009 Share Posted April 4, 2009 Dude, it's infinity. No. It's beyond. Link to comment Share on other sites More sharing options...
PokerPacker Posted April 4, 2009 Share Posted April 4, 2009 the would be 0.000000000... 1, such that that number had the same number of digits as .999999999999... 9 Link to comment Share on other sites More sharing options...
Thinking Skins Posted April 4, 2009 Share Posted April 4, 2009 we. live. in. a. continuous. world.Discrete. measures. are. not. an. accurate. portrayal. of. reality. The density of the real numbers states that between any two real numbers that are not equal there exists a third number. So if x != z, then there exists a y such that x < y < z or z < y < x. Are you claiming that .99999.... is not a real number? Link to comment Share on other sites More sharing options...
Thinking Skins Posted April 4, 2009 Share Posted April 4, 2009 and I can prove something else:-1/1=1/-1 sqrt(-1/1)=sqrt(1/-1) sqrt(-1)/sqrt(1)=sqrt(1)/sqrt(-1) i/1=1/i i*i/1=i*1/i i^2/1=i/i -1=1 ? This isn't right because you oversimplified. sqrt(-1) is not i, its plus or minus i. So you'd get (from the bold) (+/-) i / 1 = 1 / (+/-) i (+/-) i^2 / 1 = i / (+/-) i (+/-) (-1) = (+/-) 1 and now there's no contradiction. Link to comment Share on other sites More sharing options...
Spec138 Posted April 4, 2009 Share Posted April 4, 2009 and I can prove something else:-1/1=1/-1 sqrt(-1/1)=sqrt(1/-1) sqrt(-1)/sqrt(1)=sqrt(1)/sqrt(-1) i/1=1/i i*i/1=i*1/i i^2/1=i/i -1=1 ? sqrt(-1/1)=sqrt(1/-1) sqrt(-1)/sqrt(1)=sqrt(1)/sqrt(-1) Only applies if both the sqrts are positive. PROOF BUSTED! Also, to add, looks like I was wrong about infinity TS. Are you an engineer or something ? Link to comment Share on other sites More sharing options...
PokerPacker Posted April 4, 2009 Share Posted April 4, 2009 This isn't right because you oversimplified. sqrt(-1) is not i, its plus or minus i. So you'd get (from the bold) (+/-) i / 1 = 1 / (+/-) i (+/-) i^2 / 1 = i / (+/-) i (+/-) (-1) = (+/-) 1 and now there's no contradiction. no, sqrt(-1) is just i i^2 = -1 (-i)^2 = 1 Link to comment Share on other sites More sharing options...
ACW Posted April 4, 2009 Share Posted April 4, 2009 http://www.freshminds.com/animation/alan_watts_prickles.htmlTrue that. Link to comment Share on other sites More sharing options...
PokerPacker Posted April 4, 2009 Share Posted April 4, 2009 sqrt(-1/1)=sqrt(1/-1)sqrt(-1)/sqrt(1)=sqrt(1)/sqrt(-1) Only applies if both the sqrts are positive. PROOF BUSTED! Also, to add, looks like I was wrong about infinity TS. Are you an engineer or something ? ah, I figured there was probably a rule like that preventing that from happening. but until someone pointed it out, it was my false-proof. Link to comment Share on other sites More sharing options...
Spec138 Posted April 4, 2009 Share Posted April 4, 2009 ah, I figured there was probably a rule like that preventing that from happening. but until someone pointed it out, it was my false-proof. I knew it was wrong, I just couldn't prove it. Kinda like those 2=1 "proofs" Link to comment Share on other sites More sharing options...
Larry Posted April 4, 2009 Share Posted April 4, 2009 . . . a-b = 1 waah? but a = infinity and b= infinity! Congratulations. You've just proven that infinity + 1 = infinity. Link to comment Share on other sites More sharing options...
Thinking Skins Posted April 4, 2009 Share Posted April 4, 2009 I say they are equal. There's a funner geometric series proof, but I don't have time to post it now, so I'll update later. Here's one though I really like.x = .9 repeating 10x = 9.9 repeating 10x -x = 9.9 repeating - .9 repeating 9x = 9 x = 1 so 1 = .9 repeating This looks like my favorite. But I'd include the uniqueness of the identity in here, otherwise you're just saying that .9999999 repeating is an identity. This is my favorite because its simple and it proves the point. I'm kinda mad I didn't think of this. Link to comment Share on other sites More sharing options...
Touchdown Redskins Posted April 4, 2009 Share Posted April 4, 2009 Don't know if it's been posted yet, but there's a proof that I've always liked. Let x = 0.9999... Then 10x - x = 9x (clearly) But, 10x - x = 9 (because 9.9999... minus 0.9999... is clearly 9) 9 = 9x x = 1 Edit: Looks like it has been posted. Oh well. Link to comment Share on other sites More sharing options...
ACW Posted April 4, 2009 Share Posted April 4, 2009 What's his package got to do with imaginary numbers?:rotflmao: Link to comment Share on other sites More sharing options...
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