Thursday, December 17, 2009

Let x=......

Let x = [distance traveled, time it will take to travel the distance, etc.] is a very common expression in algebra. Once upon a time, our algebra instructor gave this example:

Let x = the largest number
and if x = the largest number, then x * x (x square) cannot be bigger than x
therefore x = x * x

and the only number that will fit that equation is 1

therefore, 1 is the largest number.

Which obviously was a wrong conclusion. So what went wrong here, all the logic was sound. Answer: the assumption itself was wrong. You simply cannot make x the "largest number."

Same logic can be applied to many real life situations. If everything is logical every step of the way and your conclusion is still way, way off, consider the possibility that the initial assumption was, simply, wrong.

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