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# 1 does not equal 2

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 Voting Style: Open Point System: 7 Point Started: 1/15/2008 Category: Education Updated: 9 years ago Status: Voting Period Viewed: 5,480 times Debate No: 1806
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 Pro 1=2 is a mathematically incorrect statemtent. I challenge anyone to prove otherwise. For instance, you might say: a=b a^2=ab a^2-b^2=ab-b^2 (a+b)(a-b)=b(a-b) a+b=b If a and b =1 1+1=1 2=1 This is a proof that I have seen all over this site. THIS PROOF IS INCORRECT!!! If a=b, then in the 4th line, when you divide by (a-b), you are really dividing by 0, and that goes against the rules of math. I CHALLENGE SOMEONE TO PROVE ME WRONG. I CHALLENGE SOMEONE TO PROVE THAT 1=2.Report this Argument Con Step 1; a and b > 0 Step 2: a = b Step 3: a2 = ab Step 4; a2 - b2 = ab - b2 Step 5: (a + b)(a - b) = b(a - b) Step 6: (a + b) = b Step 7: b + b = b Step 8: 2b = b Step 9; 2 = 1 ha 1=2Report this Argument Pro First off, I want to thank Idontcare for accepting this debate as his first one on this site *applause*. I shall now proceed and rip apart your proof *bows* This is my opponent's proof: Step 1; a and b > 0 Step 2: a = b Step 3: a2 = ab Step 4; a2 - b2 = ab - b2 Step 5: (a + b)(a - b) = b(a - b) Step 6: (a + b) = b Step 7: b + b = b Step 8: 2b = b Step 9; 2 = 1 ha 1=2 In step 5, by dividing by (a-b), you are dividing by zero, something that is not allowed in math. If a=b, then if you subtract one from the other, you get zero. It is a well known mathematical fact that you CANNOT, I repeat, CANNOT divide by zero. Dividing by zero will only give you an undefined answer. For instance, let us say that a=5. Therefore, according to step 2, b=5. Right? If we plug a=b=5 into step 5, we get the following: (5+5)(5-5)=5(5-5) If we divide by (5-5), like my opponent did, we get the following: [(5+5)(0)]/0=[5(0]/0 THIS IS WRONG. YOU CANNOT DIVIDE BY ZERO. THANK YOUReport this Argument Con with all honesty i knew that...... so do the rest of us and i just wanted to get this debate off the table we all know 1 cant equal two (Rolls eyes)Report this Argument
9 comments have been posted on this debate. Showing 1 through 9 records.
Posted by Idontcare 9 years ago
Where has the world come to if we can't admit we were wrong?
Posted by padfo0t 9 years ago
Posted by beem0r 9 years ago
When you prove something, it is the final result. If you start with a valid equation, and do any valid operations to both sides, you will still have a valid equation. This is not true the other way around - you can arrive at a correct equation even if you started with a bad one. This is because a function does not have multiple Y-values for the same X-value, but it can have the same X-value for the same Y-value. (performing operations on each side of an equation is like making a function). Since you're trying to prove the thing at the beginning, you're not actually proving it, since you use functions that can't be written as functions of Y (y=x^2, to be exact)
Posted by Thoreau 9 years ago
In step 3, you assume that a(b) = a2. This is untrue, as the result of your equation shows, because you haven't proved that a = b yet, merely assumed that it was true. a cannot equal b, because if you assume that the two are equal, your result is that 2 = 1.

Also, if your proof allows 2 to equal 1, you have done your proof wrong. We know this because math is a perfect system, and so it cannot be flawed.
Posted by zarul 9 years ago
Well beemor, I followed all the rules of algebra. Sqauring is perfectly fine if you do it to both sides.

On the other hand, I am assuming that 1 = 2 from the very beginning, which, is generally assumed not to be true.
Posted by padfo0t 9 years ago
Why does anyone care if 1 equals 2? What is the big deal. We all know that if one of us where to say. 7-5=1, then we would all sound stupid.
Posted by beem0r 9 years ago
za, there are two _different_ square roots for any number. 1 does not equal -1, nor does -1000 equal 1000. True, squaring them yields the same result. But they are not equal.
Posted by zarul 9 years ago
How does this look? Although I guess I'm supposing that one equals two in the first place.

1 = 2
-1 -1
________

0 = 1
-.5 -.5

________

(-.5 = .5) ^ 2
________

.25 = .25
Posted by Debater2008 9 years ago
You could have just said 1x5 is 5, whereas 2x5 is 10 so one and two are not the same. People who are saying that 1 and 2 are the same are only speaking in relation to this particular theorem, but they do not state that so it's easy to prove them wrong.
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