An attempt to divide by zero gives a contradictory result
A rule of algebra broken is dividing by zero (leading to a contradiction) and stating a finite result
Reason:
The given calculation is presented as follows;
1. a > 0, b > 0 given
2. a = b given
3. a·b = b²
4. a·b - a² = b² - a²
5. a·(b - a) = (b + a)·(b - a)
6. a = b + a
7. 0 = b
8. b = 2·b
9. 1 = 2
From line 4, the result are;
4. a·b - a² = b² - a² = 0
5. a·(b - a) = (b + a)·(b - a) = 0
On line 6, both sides where divided by (b - a) = 0, which should given an infinite result
Therefore, one rule of algebra broken is dividing by zero to get a finite result
In line 7, we have;
7. 0 = b
From 6. a = b + a, and a = b, we have;
8. b = 2·b
Therefore, line 9 should be;
9. 0 = 2·0; 0 = 0, given that we have;
1 × 0 = 0
2 × 0 = 0
∴ 1 × 0 = 2 × 0
However
In line 9., by dividing by b = 0, again, we have;
Therefore, one rule of algebra that is broken is dividing by zero and having a finite result
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