For all fans of Algebra:
Suppose x = 1 and y = 1. From this fact, it is easy to see that 2(x^2 - y^2) = 0 and that 5(x - y) = 0. Hence, 2(x^2 - y^2) = 5(x - y).
Dividing both sides of this equation by (x-y), we find that 2(x + y) = 5. But we know that (x + y) = 1 + 1 = 2. Explain to me, then, how 4 = 5.
Any ideas?
Zero is an exception to many algebraic rules that were not devised to be all-inclusive, but to suit the infinite majority of numbers.
Yes, but can you discover the wrong step?
Yes, but can you discover the wrong step?
To divide both sides by (x-y) was to divide both sides by 0. For example, 13*0 does equal 5*0, but it does not follow that 13 equals 5. The reason why it is usually effective to either multiply or divide each side by the same number is because they were equal before and remain equal. But if two unequal things become equal simply by multiplying each by the same integer, that one could expect that dividing by that number from an equality, the inverse of multiplying, will produce the inequality from which it originated. Whatever you are comparing, *none of this* and *none of that* are the same. The only way two different entities would be the same is when there is no existence, because there must be existence in order to have the potential for things to differ.
For all fans of Algebra:
Suppose x = 1 and y = 1. From this fact, it is easy to see that 2(x^2 - y^2) = 0 and that 5(x - y) = 0. Hence, 2(x^2 - y^2) = 5(x - y).
Dividing both sides of this equation by (x-y), we find that 2(x + y) = 5. But we know that (x + y) = 1 + 1 = 2. Explain to me, then, how 4 = 5.
Any ideas?