----------------------------------- blaster009 Wed May 17, 2006 10:22 pm Theoretical! ----------------------------------- Yar har har. Let's argue why or why not anything divided by ∞ is 0, and if it should work the other way. To ponder (where n is any real number): n/∞ = 0 n/0 = ∞ 0/0 = Undefined (instead of 1) ∞/∞ = Undefined (instead of 1) ----------------------------------- md Wed May 17, 2006 10:30 pm ----------------------------------- n/x as x-> ∞ = 0. Likewise n/x as x -> 0 = ∞. That's not the same as n/∞=0 or n/0 = ∞. Infinites are difficult in math... they tend to break people's minds ;) ----------------------------------- rizzix Thu May 18, 2006 10:37 am ----------------------------------- pshhht.. n/x -> 0 as x -> ∞ and n/x -> ∞ as x -> 0 ----------------------------------- codemage Thu May 18, 2006 11:09 am ----------------------------------- Infinites are difficult in math... they tend to break people's minds ;) That's because infinity doesn't really have a place in reality. It's a mathematical abstraction. Most people can't get over Zeno's paradox. ----------------------------------- Andy Thu May 18, 2006 1:16 pm ----------------------------------- the way my highschool physics teacher described it, infinity is just a sign post somewhere, once you past that sign post, you're in infinity land haha.. i miss physics :lol: ----------------------------------- Cervantes Thu May 18, 2006 4:26 pm Re: Theoretical! ----------------------------------- 0/0 = Undefined (instead of 1) I have my own little theory about this one. It represents any number. This sort of comes through when solving limits that go to 0/0. Better yet, set 0/0 to x and solve for x. x = 0/0 0x = 0 Any value of x satisfies this equation, and so 0/0 represents any number. Similarly for ∞/∞ ----------------------------------- Andy Thu May 18, 2006 5:58 pm ----------------------------------- you cant multiply both sides of an equation by 0 and use it as a valid argument ----------------------------------- MysticVegeta Thu May 18, 2006 8:53 pm ----------------------------------- yup andy is right. say: x = 0/5 5x = 0 x must be 0, other #s dont satisfy ----------------------------------- md Thu May 18, 2006 10:13 pm ----------------------------------- yup andy is right. say: x = 0/5 5x = 0 x must be 0, other #s dont satisfy Umm... that's a totally different arguement... And rizzix; that's what I said. Aproaches is not the same as equals... another thing people don't always understand. 0/0 is undefined (not 1) as you cannot divide anything by nothing (not even nothing). ∞/∞ is one because the two ∞'s cancel out (just as any two variables of the same name and power would. ----------------------------------- Cervantes Fri May 19, 2006 5:27 pm ----------------------------------- yup andy is right. say: x = 0/5 5x = 0 x must be 0, other #s dont satisfy Aw great, now I've got water all over my monitor. Well, not really, but I thought I'd say that anyways because it neatly described my reaction. If I happened to have had water in my mouth at the time, that would have been the outcome. MysticVegeta, 0/5 is 0. you cant multiply both sides of an equation by 0 and use it as a valid argument Why not? It's a tricky reason to articulate, I'm sure. Now that I've thought about it a bit more, I'm thinking you're right. My reason: multiplying both sides by zero (which is a perfectly legal operation) gives: 0x = (0 / 0) * 0 Not what I previously had: 0x = 0 which assumed that 0/0 was 1. ----------------------------------- Andy Sat May 20, 2006 1:47 pm ----------------------------------- the simplest way to look at 0/a a/0 and 0/0 is if you have 0 apples and try to split it with a people, each person gets 0 thus 0/a = 0 if you have a apples and try to split it with 0 people,we have nobody to ask about how many apples they recieved all we know is the a apples disappeared. thus a/0 is undefined and if you have 0 apples split betwen 0 people, then we cannot determine how many apples each person recieved since we had no proof of the apple, and no body to tell us what happened thus 0/0 is indeterminate ----------------------------------- Mazer Sat May 20, 2006 2:41 pm ----------------------------------- I took the apples, Andy. I took the apples, and I threw them at your windows. Then when your neighbours saw me I blamed it on the ten year old kid who happened to be riding by at the time. The police want to know if you'll be pressing charges. ----------------------------------- jamonathin Sat May 20, 2006 6:07 pm ----------------------------------- lmao mazer . . but yeah, any way your slice it, it's still going to turn out the way Andy explained it. No matter what variables you stick in there. But here's something . . Let's say n / x = 0 then n = 0x 1 = 0x / n 1 = 0 / n 1 = 0 ? Did I miss something :? or does there have to be restrictions for n (n = 0, n E R). . ----------------------------------- md Sat May 20, 2006 9:12 pm ----------------------------------- No restriction because take n = 0 n = 0x 0 = 0x 0 = 0 ----------------------------------- Martin Mon May 22, 2006 12:04 am ----------------------------------- Or we can get into exciting things to confuse people such as that 0.99.. = 1. The big problem that people have with infinities is that they think of it as a really big number, which it isn't. Infinity is a concept, not a number. There is no number that equals 'infinity,' because infinity is NOT a number. Once you get over that, it's much easier. As such, something like 1/infinity has no meaning, because you're dividing a number (1) by not a number (infinity). This makes a number of operations useless on infinity, such as addition (infinity + 1 anyone?). It's like asking what 5 + purple is - it doesn't make any sense. When you're saying 1/infinity, for the most part you're saying 1/BIG, which tends to zero as BIG gets bigger. What this means is that you can get arbitrarily close to zero - give me a positive distance to zero, and I can make it so that 1/BIG is within that distance. ----------------------------------- Andy Mon May 22, 2006 11:31 am ----------------------------------- dang it martin, i already said that! it's just a sign post, once you pass it, you're in infinity land where nothing makes sense anymore ----------------------------------- chrispminis Mon May 22, 2006 12:52 pm ----------------------------------- Lol guys ever heard of the 1=2 flaw? Illustrates the ways people illegaly abuse the number 0. ----------------------------------- Martin Mon May 22, 2006 7:07 pm ----------------------------------- dang it martin, i already said that! it's just a sign post, once you pass it, you're in infinity land where nothing makes sense anymore Mr. White has trained us well.