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Let x = y
x - y = 0
2x - 2y = 0
2x - 2y = x - y
2(x - y) = x - y
2 = 1
The fallacy is that numbers cannot be divided by zero. (
x - y = 0 )
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1 = -1
The fallacy is that
is not an ordinary (real) square root. There is no guarantee
that
is true for values of x and y that are not positive.
The real problem is that (-1)(-1) = 1 and
but
which is not equal to one.
The concept of
 does not
hold when
a and b are negative numbers.
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