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

You are not logged in. #1 20060305 04:41:52
Proof that 1 = 1Here's a simple "proof" of something impossible that one of my friends came up with in high school. Someone who really understands second year high school algebra ought to be able to see the mistake in it, but at least half the math teachers at school couldn't figure it out! Here goes. Sorry, I'll stop making equation images unless I need them for something complicated. This was just I test to see if I understood the system. #4 20060305 06:08:43
Re: Proof that 1 = 1Not entirely. "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 20060305 09:05:26
Re: Proof that 1 = 1I assume you mean a second degree polynomial equation here? There are two (though once in a while they are the same as each other). I think I see where you're going with this, but it is also quite possible to find the problem with this proof using only what we know about the properties of complex numbers. These are properties that I believe are taught in the second year of Algebra at most high schools. #6 20060305 09:37:07
Re: Proof that 1 = 1I agree with what Ricky is implying. Why did the vector cross the road? It wanted to be normal. #7 20060305 10:12:00
Re: Proof that 1 = 1Sorry I was so cryptic. I just like to let others trying to get it without being told the answer.
Well, technically, there are always two. Just because they have the same value doesn't mean they aren't two roots.
Can you be more specific? Besides the ± which mathsyperson pointed out, I see no other incorrect steps in the proof. Last edited by Ricky (20060305 10:15:06) "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..." #8 20060305 11:29:26
Re: Proof that 1 = 1Now I see what you were saying. When solving algebra equations, if you apply a square root to both sides it is then necessary to be careful to choose the correct + or  sign when you apply it, because the correct solution to your equation might only be valid in one of those cases. #9 20060305 11:46:04
Re: Proof that 1 = 1When I first went through this exercise a long time ago, it also got me thinking about more general problem solving strategies. Let's say you have a proof like this that you know is wrong but you can't figure out where the problem was introduced. If the proof was really long then it could take forever to go through it line by line to find the mistake. A good trick is to evaluate it at key points throughout your work. #10 20060305 16:02:48
Re: Proof that 1 = 1You have to be careful with that method though because you can be right for the wrong reason. But that is what I used as well. "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 20060406 08:52:59
Re: Proof that 1 = 1Hi, Last edited by kimrei (20060406 09:07:54) #12 20060406 09:37:51
Re: Proof that 1 = 1Ummm... it seems that whenever you dip your toe into "0" that kind of thing happens, and x1=0. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #13 20060409 05:21:26
Re: Proof that 1 = 1There's also this one: #14 20060409 20:18:29
Re: Proof that 1 = 1You Cannot Divide By 0. IPBLE: Increasing Performance By Lowering Expectations. #15 20060409 20:20:18
Re: Proof that 1 = 1Or,when you want to solve this parametric euation, for example: IPBLE: Increasing Performance By Lowering Expectations. #16 20060520 03:45:10
Re: Proof that 1 = 1to the first post The Beginning Of All Things To End. The End Of All Things To Come. #17 20060520 10:47:09
Re: Proof that 1 = 1You got it. In general, the fallacy that was committed was using a theorem while not meeting its preconditions first. "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..." #18 20060520 13:53:11
Re: Proof that 1 = 1or or or So we should NOT consider Last edited by liuv (20060520 14:44:29) I'm from Beijing China. my MSN: B747_400F@HOTMAIL.COM 