Ill preface this discussion by stating straightforward that my knowledge of mathematics is rudimentary at best, and my expertise lies in the most basic algebra. That said, Ive concluded that fundamental math is flawed. This observation renders the teaching of math in any educational institution completely unnecessary, and, in addition, changes the manner in which man views his world. Allow me to propose my argument.
Take a standard polynomial equation, ax2 + bx + c = 0. For the sake of clarity, well plug in some arbitrary numbers x2 + 5x + 6 = 0.
Since we know the entire equation equals zero, we can freely add the equation to itself on either side as many times as we like, since were adding nothing. Adding it to the right side, we get x2 + 5x + 6 = 0 + x2 + 5x + 6.
Since its just adding zero, we might as well do it again. Lets again add the equation (which equals zero) the right side. That gives us x2 + 5x + 6 = 0 + x2 + 5x + 6 + x2 + 5x + 6, or x2 + 5x + 6 = 0 + 2(x2 + 5x + 6). We might as well go ahead and take out that zero since it doesnt matter, so that leaves us with x2 + 5x + 6 = 2(x2 + 5x + 6).
Suddenly, we see that the left side is equal to itself times two. The equation can be written like this: 1(x2 + 5x + 6) = 2(x2 + 5x + 6), and we see that the areas in parenthesis are the same, so we can divide those out, leaving us with 1 = 2.
Oh, but wait. Heres a problem, you say? What we are dividing out is equal to zero, and therefore cannot be placed in the denominator? This is not only incorrect, but fundamentally absurd. The problem lies in the very basic principles of mathematics. In dividing zero by zero, we are not left with something which is undefined. In actuality, it is quite definable it is infinity. Division is the act of dividing a number, and just as ten may be divided by five to yield two, nothing (zero) is divided by nothing to yield infinity, since nothing can be placed into nothing infinite times. Five two times is ten, just as zero infinite times is still zero. Furthermore, any number divided by zero is not undefined, but instead equals infinity, since nothing may be placed into any amount an infinite amount of times.
Math, at its crudest level, expects the user to concede that it is impossible to define zero placed into zero, and it is on this assumption that all else is based. If we fail to accept this clear fallacy, we fail to accept math. We can add x2 + 5x + 6 even more times to our equation, dividing it out, in order to make 1 = 3, 2 = 4, etc. No longer is any number assigned its own value everything is equal. Math explodes.