teaching complex numbers in high school
... Suppose that i ϵ R. Then we know that i is greater than zero, equal to zero, or less than
zero. If we take i to be greater than zero, then i2 = i ∙ i > 0 since the product of two positive
numbers is positive. That is, -1 > 0 which is false. Therefore, i cannot greater than 0.
Similar contradictions ...