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take 2 numbers a and b. a is equal to b.

a=b

1) Multiply both sides of the equation by the same number and both sides are still equal (axiom of multiplication):

a**2=ab

2) Subtract both sides of the equation by the same number and both sides are still equal (axiom of subtraction):

a**2-b**2=ab-b**2

3) Factoring yields

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

4) Multiply both sides of the equation by the same number and both sides are still equal (axiom of multiplication):

(a+b)(a-b)(a-b)**-1=b(a-b)(a-b)**-1

5) Canceling out like terms yields

a+b=b

Therefore 2=1

Of couse, there is an obvious mistake in this theorem, which is easy to find. LOL.