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Impossible math 1


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For a certain class I had to prove 25-30 things in math that are impossible. I was the only one in my class to do so. Since then I thought of more and I was shown more.

Here is the first of a a number of them

given

a = b

a = 1

-----

a^2 = ab (where ^ = raised to the power)

a^2 -b^2 = ab - b^2

factor it out:

(a+B)(a-B) = b(a-B)

divide through by a-b

a+b = b

1 + 1 = 1

2 = 1

What is the flaw with this?

What is a-b?

When you divide through by a-b you are actually dividing through by 0 which is impossible

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Sort of.

The famous one works a bit differently with the same fundamental flaw.

1. a = b + 1

2. (a-B.)a = (a-B.)(b+1)

3. a2 - ab = ab + a - b2 - b

4. a2 - ab -a = ab + a -a - b2 - b

5. a(a - b - 1) = b(a - b - 1)

6. a = b

7. b + 1 = b

8. Therefore, 1 = 0

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Well, the Zero Proof is a bit different:

a = b

a^2 = ab

a^2 - b^2 = ab - b^2

(difference of two squares)

(a+B.)(a-B.) = ab - b^2

(a+B.)(a-B.) = b(a-B.)

a+b = b

a = 0

A does not have any fixed value (no a = 1 (or any other number) step), it is just an unknown. Making you wonder how ANY NUMBER AT ALL could equal 0. Of course the step dividing by (a-B) is wrong as a-b is 0 because a=b.

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