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proof of 2=1
i learned this in my ap calculus ab class
there is a flaw in the equation but it is still kinda neat to me i will tell you guys the flaw later so that some of you can try to figure it out on your own here goes... ...............equation :": reason .............a=b.........:": given (a not equal to 0) .........a^2=ab........:": multiplication property of equality ..a^2-b^2=ab-b^2.:": subtraction property of equality (a-b)(a+b)=b(a-b)...:": factoring .........a+b=b..........:": division property of equality .........b+b=b..........:": substitution ...........2b=b..........:": simplify ............2=1...........:": division property of equality |
Re: proof of 2=1
You can't divide by (a-b) because that is equal to 0. If a=b, then a-b=0, and you can't divide by 0. I learned this too last year in my Calculus AB class, but I also learned another way involving square roots and imaginary numbers.
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Re: proof of 2=1
Division property of equality doesn't hold here since a=b so you're dividing by 0. Everyone probably knows the "trick" to this one by now, unfortunately.
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Re: proof of 2=1
i didnt get to edit it in time to say not to post the answer... oh well
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Re: proof of 2=1
Sorry about ruining it. I thought you were asking if any of us COULD figure it out. Here's the other one I learned. This one too is fallacious, but I'll leave it to you guys to find where it is wrong.
Let's start off with two versions of -1 equal to each other: 1/-1 = -1/1 Now, we'll take the square root of both sides: SQRT(1/-1) = SQRT(-1/1) Now, let's simplify this: SQRT(1)/SQRT(-1) = SQRT(-1)/SQRT(1) Again, to further simplify this. Also, we'll substitute i for SQRT(-1): 1/i = i/1 Now, we'll divide each side by 2: 1/2i = i/2 Now, let's add (3/2i) to each side of the equation: (1/2i) + (3/2i) = (i/2) + (3/2i) Now, we'll multiply both sides by i: i{(1/2i) + (3/2i)} = i{(i/2) + (3/2i)} Now, let's substitute that i into the equation: (i/2i) + (3i/2i) = (i^2/2) + (3i/2i) Now, we'll simplify the equation once again. Know that i/i is 1 and i^2 is -1: 1/2 + 3/2 = -1/2 + 3/2 This leads us to our final equation: 2 = 1 |
Re: proof of 2=1
Old and not worthy of Critical Thinking.
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