Today, to have some fun, I'm going to prove something wrong. The challenge today won't be to find the right answer, but to find the flaw in the answer.
Prove: 5 = 7
Well, it looks impossible and wrong at first, but let's try anyway.
Let a = b
Multiply both sides by a and add a2 - 2a to both sides:
2a2 - 2ab = a2 - ab
Take 2 as a common factor:
2(a2 - ab) = a2 - ab
Divide by a2 - ab:
2 = 1
Multiply by 2:
4 = 2
Add 3 to both sides:
7 = 5
By the reflexive property of equality:
5 = 7
Q.E.D.
Obviously, there is something wrong with this proof, and detailed reading will find it. One step was eliminated from this proof. As you can see, after the first assignment of variables (a = b), two steps were done at once. When you break down the steps, you find that a2 = ab. This leads to a2 - ab = 0, which shows us that the step that led to 2 = 1 was division by zero.
Now you can all understand why the first commandment of math is "Thou shalt not divide by zero". Division by zero can prove anything and destroy mathematic foundations. Only divide by non-zero numbers.
Nadav
nadavs
Wednesday, July 9, 2008
The Impossible Proof
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2 comments:
divide by 0 error.
you stated that a=b.
and then divided by something containing a and b that have the total of 0. this is an old problem.
cheers.
In the second step you multiplied a to both sides which results in a2=ab
and then u added a2-2a to both sides which result in
a2+a2-2a=a2-2a+ab
you are wrong there
NOTE A2 means a square
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